WorldWideScience

Sample records for non-perturbative statistical theory

  1. On perturbation theory for distance dependent statistics.

    Energy Technology Data Exchange (ETDEWEB)

    Mashkevich, S V

    1994-12-31

    It is known that perturbation theory for anyons has to be modified near Bose statistics in order to get correct finite results. For ``distance dependent statistics`` or anyons with smeared flux tubes, perturbation theory is in principle applicable directly but gives results which hold for too small values of the statistical parameter and, in particular, are not valid as the flux tube radius tends to zero. In this paper we discuss the way to modify perturbation theory for this situation, which allows to obtain the appropriate results. (author). 6 refs.

  2. Non-perturbative field theory/field theory on a lattice

    International Nuclear Information System (INIS)

    Ambjorn, J.

    1988-01-01

    The connection between the theory of critical phenomena in statistical mechanics and the renormalization of field theory is briefly outlined. The way of using this connection is described to get information about non-perturbative quantities in QCD and about more intelligent ways of doing the Monte Carlo (MC) simulations. The (MC) method is shown to be a viable one in high energy physics, but it is not a good substitute for an analytic understanding. MC-methods will be very valuable both for getting out hard numbers and for testing the correctness of new ideas

  3. Non-hard sphere thermodynamic perturbation theory.

    Science.gov (United States)

    Zhou, Shiqi

    2011-08-21

    A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. © 2011 American Institute of Physics

  4. Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory

    Science.gov (United States)

    Matsubara, Takahiko

    2003-02-01

    We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.

  5. Introduction to non-perturbative heavy quark effective theory

    International Nuclear Information System (INIS)

    Sommer, R.

    2010-08-01

    My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti Λ and λ 1 lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m) n+1 if the theory was treated including (1/m) n terms. Clearly, the weakest point of HQET is that it intrinsically is an expansion. In practise, carrying it

  6. Introduction to non-perturbative heavy quark effective theory

    Energy Technology Data Exchange (ETDEWEB)

    Sommer, R. [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2010-08-15

    My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti {lambda} and {lambda}{sub 1} lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m){sup n+1} if the theory was treated including (1/m){sup n} terms. Clearly, the weakest point of HQET is that it

  7. Cumulants in perturbation expansions for non-equilibrium field theory

    International Nuclear Information System (INIS)

    Fauser, R.

    1995-11-01

    The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system. (orig.)

  8. Non-perturbative aspects of string theory from elliptic curves

    International Nuclear Information System (INIS)

    Reuter, Jonas

    2015-08-01

    We consider two examples for non-perturbative aspects of string theory involving elliptic curves. First, we discuss F-theory on genus-one fibered Calabi-Yau manifolds with the fiber being a hypersurface in a toric fano variety. We discuss in detail the fiber geometry in order to find the gauge groups, matter content and Yukawa couplings of the corresponding supergravity theories for the four examples leading to gauge groups SU(3) x SU(2) x U(1), SU(4) x SU(2) x SU(2)/Z 2 , U(1) and Z 3 . The theories are connected by Higgsings on the field theory side and conifold transitions on the geometry side. We extend the discussion to the network of Higgsings relating all theories stemming from the 16 hypersurface fibrations. For the models leading to gauge groups SU(3) x SU(2) x U(1), SU(4) x SU(2) x SU(2)/Z 2 and U(1) we discuss the construction of vertical G 4 fluxes. Via the D3-brane tadpole cancelation condition we can restrict the minimal number of families in the first two of these models to be at least three. As a second example for non-perturbative aspects of string theory we discuss a proposal for a non-perturbative completion of topological string theory on local B-model geometries. We discuss in detail the computation of quantum periods for the examples of local F 1 , local F 2 and the resolution of C 3 /Z 5 . The quantum corrections are calculated order by order using second order differential operators acting on the classical periods. Using quantum geometry we calculate the refined free energies in the Nekrasov-Shatashvili limit. Finally we check the non-perturbative completion of topological string theory for the geometry of local F 2 against numerical calculations.

  9. Divergence of perturbation theory in large scale structures

    Science.gov (United States)

    Pajer, Enrico; van der Woude, Drian

    2018-05-01

    We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White [1], and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.

  10. Probing non-perturbative effects in M-theory

    International Nuclear Information System (INIS)

    Hatsuda, Yasuyuki; Okuyama, Kazumi

    2014-07-01

    The AdS/CFT correspondence enables us to probe M-theory on various backgrounds from the corresponding dual gauge theories. Here we investigate in detail a three-dimensional U(N) N=4 super Yang-Mills theory coupled to one adjoint hypermultiplet and N f fundamental hypermultiplets, which is large N dual to M-theory on AdS 4 x S 7 /Z N f . Using the localization and the Fermi-gas formulation, we explore non-perturbative corrections to the partition function. As in the ABJM theory, we find that there exists a non-trivial pole cancellation mechanism, which guarantees the theory to be well-defined, between worldsheet instantons and membrane instantons for all rational (in particular, physical or integral) values of N f .

  11. On estimating perturbative coefficients in quantum field theory and statistical physics

    International Nuclear Information System (INIS)

    Samuel, M.A.; Stanford Univ., CA

    1994-05-01

    The authors present a method for estimating perturbative coefficients in quantum field theory and Statistical Physics. They are able to obtain reliable error-bars for each estimate. The results, in all cases, are excellent

  12. Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation

    Directory of Open Access Journals (Sweden)

    Samuel Friot

    2010-10-01

    Full Text Available Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional φ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.

  13. Non-perturbative heavy quark effective theory. Introduction and status

    International Nuclear Information System (INIS)

    Sommer, Rainer; Humboldt-Universitaet, Berlin

    2015-01-01

    We give an introduction to Heavy Quark Effective Theory (HQET). Our emphasis is on its formulation non-perturbative in the strong coupling, including the non-perturbative determination of the parameters in the HQET Lagrangian. In a second part we review the present status of HQET on the lattice, largely based on work of the ALPHA collaboration in the last few years. We finally discuss opportunities and challenges.

  14. Non-Perturbative Renormalization

    CERN Document Server

    Mastropietro, Vieri

    2008-01-01

    The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi

  15. New Methods in Non-Perturbative QCD

    Energy Technology Data Exchange (ETDEWEB)

    Unsal, Mithat [North Carolina State Univ., Raleigh, NC (United States)

    2017-01-31

    In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), and there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.

  16. A non-perturbative study of massive gauge theories

    DEFF Research Database (Denmark)

    Della Morte, Michele; Hernandez, Pilar

    2013-01-01

    and the lightest degrees of freedom are spin one vector particles with the same quantum numbers as the conserved current, we argue that the most general effective theory describing their low-energy dynamics must be a massive gauge theory. We present results of a exploratory numerical simulation of the model......We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists...... and find indications for the presence of a scaling region where both a triplet vector and a scalar remain light....

  17. Alien calculus and non perturbative effects in Quantum Field Theory

    Science.gov (United States)

    Bellon, Marc P.

    2016-12-01

    In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.

  18. Cosmological perturbation theory and quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)

    2016-08-04

    It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.

  19. Connection between perturbation theory, projection-operator techniques, and statistical linearization for nonlinear systems

    International Nuclear Information System (INIS)

    Budgor, A.B.; West, B.J.

    1978-01-01

    We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation

  20. Geometric perturbation theory and plasma physics

    International Nuclear Information System (INIS)

    Omohundro, S.M.

    1985-01-01

    Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations

  1. Non-perturbative effects in supersymmetry

    International Nuclear Information System (INIS)

    Veneziano, G.

    1987-01-01

    Some non perturbative aspects of globally supersymmetric (SUSY) gauge theories are discussed. These share with their non-supersymmetric analogues interesting non perturbative features, such as the spontaneous breaking of chiral symmetries via condensates. What is peculiar about supersymmetric theories, however, is that one is able to say a lot about non-perturbative effects even without resorting to elaborate numerical calculations: general arguments, supersymmetric and chiral Ward identities and analytic, dynamical calculations will turn out to effectively determine most of the supersymmetric vacuum properties. 28 references, 5 figures

  2. Large-order perturbation theory

    International Nuclear Information System (INIS)

    Wu, T.T.

    1982-01-01

    The original motivation for studying the asymptotic behavior of the coefficients of perturbation series came from quantum field theory. An overview is given of some of the attempts to understand quantum field theory beyond finite-order perturbation series. At least is the case of the Thirring model and probably in general, the full content of a relativistic quantum field theory cannot be recovered from its perturbation series. This difficulty, however, does not occur in quantum mechanics, and the anharmonic oscillator is used to illustrate the methods used in large-order perturbation theory. Two completely different methods are discussed, the first one using the WKB approximation, and a second one involving the statistical analysis of Feynman diagrams. The first one is well developed and gives detailed information about the desired asymptotic behavior, while the second one is still in its infancy and gives instead information about the distribution of vertices of the Feynman diagrams

  3. EDITORIAL: Non-linear and non-Gaussian cosmological perturbations Non-linear and non-Gaussian cosmological perturbations

    Science.gov (United States)

    Sasaki, Misao; Wands, David

    2010-06-01

    In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.

  4. Modeling of aqueous electrolyte solutions with perturbed-chain statistical associated fluid theory

    DEFF Research Database (Denmark)

    Cameretti, Luca F.; Sadowski, Gabriele; Mollerup, Jørgen

    2005-01-01

    The vapor pressures and liquid densities of single-salt electrolyte solutions containing NaCl, LiCl, KCl, NaBr, LiBr, KBr, NaI, LiI, KI, Li2SO4, Na2SO4, and K2SO4 were modeled with an equation of state based on perturbed-chain statistical associated fluid theory (PC-SAFT). The PC-SAFT model...

  5. Non-perturbative Green functions in quantum gauge theories

    International Nuclear Information System (INIS)

    Shabanov, S.V.

    1991-01-01

    Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tensing to zero at spatial infinity. 20 refs

  6. Topological string theory, modularity and non-perturbative physics

    Energy Technology Data Exchange (ETDEWEB)

    Rauch, Marco

    2011-09-15

    In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques of direct integration known from topological string theory can be used to solve the closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, explicit expressions for the ring of non-holomorphic modular forms that are needed to express all closed matrix model amplitudes are given. This allows to integrate the holomorphic anomaly equation up to holomorphic modular terms that are fixed by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the non-holomorphic modular ring of the group {gamma}(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. Using these results it is possible to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, it is argued that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model. In the second part a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi-Yau manifold is derived using wall-crossing formulae and the theory of mock modular forms. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4- D2-D0 brane systems. The compatibility of this equation with anomaly equations previously observed in the context of N=4 topological Yang-Mills theory on P{sup 2} and E-strings obtained from wrapping M5-branes on a del Pezzo surface which in

  7. Topological string theory, modularity and non-perturbative physics

    International Nuclear Information System (INIS)

    Rauch, Marco

    2011-09-01

    In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques of direct integration known from topological string theory can be used to solve the closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, explicit expressions for the ring of non-holomorphic modular forms that are needed to express all closed matrix model amplitudes are given. This allows to integrate the holomorphic anomaly equation up to holomorphic modular terms that are fixed by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the non-holomorphic modular ring of the group Γ(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. Using these results it is possible to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, it is argued that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model. In the second part a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi-Yau manifold is derived using wall-crossing formulae and the theory of mock modular forms. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4- D2-D0 brane systems. The compatibility of this equation with anomaly equations previously observed in the context of N=4 topological Yang-Mills theory on P 2 and E-strings obtained from wrapping M5-branes on a del Pezzo surface which in turn is

  8. Perturbation theory of effective Hamiltonians

    International Nuclear Information System (INIS)

    Brandow, B.H.

    1975-01-01

    This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)

  9. Calibrated geometries and non perturbative superpotentials in M-theory

    International Nuclear Information System (INIS)

    Hernandez, R.

    1999-12-01

    We consider non perturbative effects in M-theory compactifications on a seven-manifold of G 2 holonomy arising from membranes wrapped on supersymmetric three-cycles. When membranes are wrapped on associative submanifolds they induce a superpotential that can be calculated using calibrated geometry. This superpotential is also derived from compactification on a seven-manifold, to four dimensional Anti-de Sitter spacetime, of eleven dimensional supergravity with non vanishing expectation value of the four-form field strength. (author)

  10. The b-quark mass from non-perturbative $N_f=2$ Heavy Quark Effective Theory at $O(1/m_h)$

    DEFF Research Database (Denmark)

    Bernardoni, F.; Blossier, B.; Bulava, J.

    2014-01-01

    We report our final estimate of the b-quark mass from $N_f=2$ lattice QCD simulations using Heavy Quark Effective Theory non-perturbatively matched to QCD at $O(1/m_h)$. Treating systematic and statistical errors in a conservative manner, we obtain $\\overline{m}_{\\rm b}^{\\overline{\\rm MS}}(2 {\\rm...

  11. Geometric Hamiltonian structures and perturbation theory

    International Nuclear Information System (INIS)

    Omohundro, S.

    1984-08-01

    We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging

  12. Dynamical generation of non-abelian gauge group via the improved perturbation theory

    International Nuclear Information System (INIS)

    Kuroki, Tsunehide

    2008-01-01

    It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua. (author)

  13. Perturbation theory in large order

    International Nuclear Information System (INIS)

    Bender, C.M.

    1978-01-01

    For many quantum mechanical models, the behavior of perturbation theory in large order is strikingly simple. For example, in the quantum anharmonic oscillator, which is defined by -y'' + (x 2 /4 + ex 4 /4 - E) y = 0, y ( +- infinity) = 0, the perturbation coefficients, A/sub n/, in the expansion for the ground-state energy, E(ground state) approx. EPSILON/sub n = 0//sup infinity/ A/sub n/epsilon/sup n/, simplify dramatically as n → infinity: A/sub n/ approx. (6/π 3 )/sup 1/2/(-3)/sup n/GAMMA(n + 1/2). Methods of applied mathematics are used to investigate the nature of perturbation theory in quantum mechanics and show that its large-order behavior is determined by the semiclassical content of the theory. In quantum field theory the perturbation coefficients are computed by summing Feynman graphs. A statistical procedure in a simple lambda phi 4 model for summing the set of all graphs as the number of vertices → infinity is presented. Finally, the connection between the large-order behavior of perturbation theory in quantum electrodynamics and the value of α, the charge on the electron, is discussed. 7 figures

  14. Non-perturbative aspects of quantum field theory. From the quark-gluon plasma to quantum gravity

    International Nuclear Information System (INIS)

    Christiansen, Nicolai

    2015-01-01

    In this dissertation we investigate several aspects of non-perturbative quantum field theory. Two main parts of the thesis are concerned with non-perturbative renormalization of quantum gravity within the asymptotic safety scenario. This framework is based on a non-Gaussian ultraviolet fixed point and provides a well-defined theory of quantized gravity. We employ functional renormalization group (FRG) techniques that allow for the study of quantum fields even in strongly coupled regimes. We construct a setup for the computation of graviton correlation functions and analyze the ultraviolet completion of quantum gravity in terms of the properties of the two- and three point function of the graviton. Moreover, the coupling of gravity to Yang-Mills theories is discussed. In particular, we study the effects of graviton induced interactions on asymptotic freedom on the one hand, and the role of gluonic fluctuations in the gravity sector on the other hand. The last subject of this thesis is the physics of the quark-gluon plasma. We set-up a general non-perturbative strategy for the computation of transport coefficients in non-Abelian gauge theories. We determine the viscosity over entropy ratio η/s in SU(3) Yang-Mills theory as a function of temperature and estimate its behavior in full quantum chromodynamics (QCD).

  15. Non-gaussianity versus nonlinearity of cosmological perturbations.

    Science.gov (United States)

    Verde, L

    2001-06-01

    Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

  16. On the non-perturbative effects

    International Nuclear Information System (INIS)

    Manjavidze, J.; Voronyuk, V.

    2004-01-01

    The quantum correspondence principle based on the time reversibility is adopted to take into account the non-Abelian symmetry constrains. The main properties of the new strong-coupling perturbation theory which take into account non-perturbative effects are described. (author)

  17. Geometric perturbation theory and plasma physics

    Energy Technology Data Exchange (ETDEWEB)

    Omohundro, S.M.

    1985-04-04

    Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.

  18. Geometric perturbation theory and plasma physics

    International Nuclear Information System (INIS)

    Omohundro, S.M.

    1985-01-01

    Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism

  19. Liquid theory with high accuracy and broad applicability: Coupling parameter series expansion and non hard sphere perturbation strategy

    Directory of Open Access Journals (Sweden)

    Shiqi Zhou

    2011-12-01

    Full Text Available Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426 1st-order high temperature series expansion (HTSE TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861, have some serious shortcomings: (i the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE and a non hard sphere (HS perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii We give a quantitative analysis on why

  20. A non-perturbative analysis in finite volume gauge theory

    International Nuclear Information System (INIS)

    Koller, J.; State Univ. of New York, Stony Brook; Van Baal, P.; State Univ. of New York, Stony Brook

    1988-01-01

    We discuss SU(2) gauge theory on a three-torus using a finite volume expansion. Our discovery of natural coordinates allows us to obtain continuum results in a region where Monte Carlo data are also available. The obtained results agree well with the perturbative and semiclassical analysis for small volumes, and there is fair agreement with the Monte Carlo results in intermediate volumes. The simple picture which emerges for the approximate low energy dynamics is that of three interacting particles enclosed in a sphere, with zero total 'angular momentum'. The validity of an adiabatic approximation is investigated. The fundamentally new understanding gained, is that non-perturbative dynamics can be incorporated by imposing boundary conditions which arise through the nontrivial topology of configuration space. (orig.)

  1. Evaluation of the truncated perturbed chain-polar statistical associating fluid theory for complex mixture fluid phase equilibria

    DEFF Research Database (Denmark)

    Karakatsani, Eirini; Kontogeorgis, Georgios; Economou, Ioannis

    2006-01-01

    Perturbed chain-statistical associating fluid theory (PC-SAFT) was extended rigorously to polar fluids based on the theory of Stell and co-workers [Mol. Phys. 1977, 33, 987]. The new PC-PSAFT was simplified to truncated PC-PSAFT (tPC-PSAFT) so that it can be practical for real polar fluid...

  2. Solitonic Integrable Perturbations of Parafermionic Theories

    CERN Document Server

    Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L

    1997-01-01

    The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.

  3. Quantum fields in the non-perturbative regime. Yang-Mills theory and gravity

    International Nuclear Information System (INIS)

    Eichhorn, Astrid

    2011-01-01

    In this thesis we study candidates for fundamental quantum field theories, namely non-Abelian gauge theories and asymptotically safe quantum gravity. Whereas the first ones have a stronglyinteracting low-energy limit, the second one enters a non-perturbative regime at high energies. Thus, we apply a tool suited to the study of quantum field theories beyond the perturbative regime, namely the Functional Renormalisation Group. In a first part, we concentrate on the physical properties of non-Abelian gauge theories at low energies. Focussing on the vacuum properties of the theory, we present an evaluation of the full effective potential for the field strength invariant F μν F μν from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the β function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators and derive an upper bound on their scaling exponents. We then consider the theory at finite temperature and study the nature of the confinement phase transition in d = 3+1 dimensions in various non-Abelian gauge theories. For SU(N) with N= 3,..,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. Our studies shed light on the question which property of a gauge group determines the order of the phase transition. In a second part we consider asymptotically safe quantum gravity. Here, we focus on the Faddeev-Popov ghost sector of the theory, to study its properties in the context of an interacting UV regime. We investigate several truncations, which all lend support to the conjecture that gravity may be asymptotically safe. In a first truncation, we study the ghost anomalous dimension which we find to be negative at the

  4. Non-integrable quantum field theories as perturbations of certain integrable models

    International Nuclear Information System (INIS)

    Delfino, G.; Simonetti, P.

    1996-03-01

    We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ T c and the scaling region around the minimal model M 2 , τ . For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalization of their Hamiltonian. (author). 41 refs, 9 figs, 1 tab

  5. Large N non-perturbative effects in N=4 superconformal Chern-Simons theories

    International Nuclear Information System (INIS)

    Hatsuda, Yasuyuki; Honda, Masazumi; Okuyama, Kazumi

    2015-07-01

    We investigate the large N instanton effects of partition functions in a class of N = 4 circular quiver Chern-Simons theories on a three-sphere. Our analysis is based on the supersymmetry localization and the Fermi-gas formalism. The resulting matrix model can be regarded as a two-parameter deformation of the ABJM matrix model, and has richer non-perturbative structures. Based on a systematic semi-classical analysis, we find analytic expressions of membrane instanton corrections. We also exactly compute the partition function for various cases and find some exact forms of worldsheet instanton corrections, which appear as quantum mechanical non-perturbative corrections in the Fermi-gas system.

  6. Non-perturbative versus perturbative renormalization of lattice operators

    International Nuclear Information System (INIS)

    Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.

    1995-09-01

    Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)

  7. Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges

    Science.gov (United States)

    Pereira, A. D.; Sobreiro, R. F.; Sorella, S. P.

    2016-10-01

    In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi: 10.1103/PhysRevD.92.045039 arXiv:1506.06995 [hep-th], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions.

  8. Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges

    International Nuclear Information System (INIS)

    Pereira, A.D.; Sobreiro, R.F.; Sorella, S.P.

    2016-01-01

    In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)

  9. Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)

    2016-10-15

    In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)

  10. Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic

    International Nuclear Information System (INIS)

    Chingangbam, Pravabati; Park, Changbom

    2009-01-01

    We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter g NL . The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of g NL and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for g NL > 0 and less of both for g NL NL and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of g NL that are clearly distinct from the quadratic order perturbations, encoded in the parameter f NL . Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between g NL and f NL type non-Gaussianities

  11. Quantum fields in the non-perturbative regime. Yang-Mills theory and gravity

    Energy Technology Data Exchange (ETDEWEB)

    Eichhorn, Astrid

    2011-09-06

    In this thesis we study candidates for fundamental quantum field theories, namely non-Abelian gauge theories and asymptotically safe quantum gravity. Whereas the first ones have a stronglyinteracting low-energy limit, the second one enters a non-perturbative regime at high energies. Thus, we apply a tool suited to the study of quantum field theories beyond the perturbative regime, namely the Functional Renormalisation Group. In a first part, we concentrate on the physical properties of non-Abelian gauge theories at low energies. Focussing on the vacuum properties of the theory, we present an evaluation of the full effective potential for the field strength invariant F{sub {mu}}{sub {nu}}F{sup {mu}}{sup {nu}} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the {beta} function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators and derive an upper bound on their scaling exponents. We then consider the theory at finite temperature and study the nature of the confinement phase transition in d = 3+1 dimensions in various non-Abelian gauge theories. For SU(N) with N= 3,..,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. Our studies shed light on the question which property of a gauge group determines the order of the phase transition. In a second part we consider asymptotically safe quantum gravity. Here, we focus on the Faddeev-Popov ghost sector of the theory, to study its properties in the context of an interacting UV regime. We investigate several truncations, which all lend support to the conjecture that gravity may be asymptotically safe. In a first truncation, we study the ghost anomalous dimension

  12. Perturbative coherence in field theory

    International Nuclear Information System (INIS)

    Aldrovandi, R.; Kraenkel, R.A.

    1987-01-01

    A general condition for coherent quantization by perturbative methods is given, because the basic field equations of a fild theory are not always derivable from a Lagrangian. It's seen that non-lagrangian models way have well defined vertices, provided they satisfy what they call the 'coherence condition', which is less stringent than the condition for the existence of a Lagrangian. They note that Lagrangian theories are perturbatively coherent, in the sense that they have well defined vertices, and that they satisfy automatically that condition. (G.D.F.) [pt

  13. Two-dimensional sigma models: modelling non-perturbative effects of gauge theories

    International Nuclear Information System (INIS)

    Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.

    1984-01-01

    The review is devoted to a discussion of non-perturbative effects in gauge theories and two-dimensional sigma models. The main emphasis is put on supersymmetric 0(3) sigma model. The instanton-based method for calculating the exact Gell-Mann-Low function and bifermionic condensate is considered in detail. All aspects of the method in simplifying conditions are discussed. The basic points are: the instanton measure from purely classical analysis; a non-renormalization theorem in self-dual external fields; existence of vacuum condensates and their compatibility with supersymmetry

  14. A non-perturbative study of 4d U(1) non-commutative gauge theory - the fate of one-loop instability

    International Nuclear Information System (INIS)

    Bietenholz, Wolfgang; Nishimura, Jun; Susaki, Yoshiaki; Volkholz, Jan

    2006-01-01

    Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d = 2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter θ, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on θ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking

  15. Perturbation theory

    International Nuclear Information System (INIS)

    Bartlett, R.; Kirtman, B.; Davidson, E.R.

    1978-01-01

    After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references

  16. Generalized ensemble theory with non-extensive statistics

    Science.gov (United States)

    Shen, Ke-Ming; Zhang, Ben-Wei; Wang, En-Ke

    2017-12-01

    The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' q -average of physical quantities, the sum ∑ pjq, is independent of the probability pi for Tsallis parameter q. The self-referential problem in the deduced probability and thermal quantities in non-extensive statistics is thus avoided, and thermodynamical relationships are obtained in a consistent and natural way. We also extend the study to the non-extensive grand canonical ensemble theory and obtain the q-deformed Bose-Einstein distribution as well as the q-deformed Fermi-Dirac distribution. The theory is further applied to the generalized Planck law to demonstrate the distinct behaviors of the various generalized q-distribution functions discussed in literature.

  17. Perturbative algebraic quantum field theory at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Lindner, Falk

    2013-08-15

    We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.

  18. Perturbative algebraic quantum field theory at finite temperature

    International Nuclear Information System (INIS)

    Lindner, Falk

    2013-08-01

    We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.

  19. Perturbative expansion of Chern-Simons theory with non-compact gauge group

    International Nuclear Information System (INIS)

    Bar-Natan, D.; Witten, E.

    1991-01-01

    Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly 'unitary' format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified. (orig.)

  20. Non-perturbative Heavy Quark Effective Theory

    DEFF Research Database (Denmark)

    Della Morte, Michele; Heitger, Jochen; Simma, Hubert

    2015-01-01

    We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B...

  1. Perturbative analysis of non-Abelian Aharonov-Bohm scattering

    International Nuclear Information System (INIS)

    Bak, D.; Bergman, O.

    1995-01-01

    We perform a perturbative analysis of the non-Abelian Aharonov-Bohm problem to one loop in the framework of a local field theory, and show the necessity of contact interactions for renormalizability of perturbation theory. Moreover at critical values of the contact interaction strength the theory is finite and preserves classical conformal invariance

  2. A non-perturbative study of 4d U(1) non-commutative gauge theory — the fate of one-loop instability

    Science.gov (United States)

    Bietenholz, Wolfgang; Nishimura, Jun; Susaki, Yoshiaki; Volkholz, Jan

    2006-10-01

    Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d = 2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter θ, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on θ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.

  3. Singular perturbation theory for interacting fermions in two dimensions

    International Nuclear Information System (INIS)

    Chubukov, A.V.; Maslov, D.L.; Gangadharaiah, S.; Glazman, L.I.

    2004-11-01

    We consider a system of interacting fermions in two dimensions beyond the second-order perturbation theory in the interaction. It is shown that the mass-shell singularities in the self-energy, arising already at the second order of the perturbation theory, manifest a nonperturbative effect: an interaction with the zero-sound mode. Resuming the perturbation theory for a weak, short-range interaction and accounting for a finite curvature of the fermion spectrum, we eliminate the singularities and obtain the results for the quasi-particle self-energy and the spectral function to all orders in the interaction with the zero-sound mode. A threshold for emission of zero-sound waves leads a non-monotonic variation of the self-energy with energy (or momentum) near the mass shell. Consequently, the spectral function has a kink-like feature. We also study in detail a non-analytic temperature dependence of the specific heat, C(T) ∝T 2 . It turns out that although the interaction with the collective mode results in an enhancement of the fermion self-energy, this interaction does not affect the non-analytic term in C(T) due to a subtle cancellation between the contributions from the real and imaginary parts of the self-energy. For a short-range and weak interaction, this implies that the second-order perturbation theory suffices to determine the non-analytic part of C(T). We also obtain a general form of the non-analytic term in C(T), valid for the case of a generic Fermi liquid, i.e., beyond the perturbation theory. (author)

  4. Non-perturbative effects and the refined topological string

    Energy Technology Data Exchange (ETDEWEB)

    Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematiques; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics

    2013-06-15

    The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P{sup 1} x P{sup 1}, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.

  5. New Results in {mathcal {N}}=2 N = 2 Theories from Non-perturbative String

    Science.gov (United States)

    Bonelli, Giulio; Grassi, Alba; Tanzini, Alessandro

    2018-03-01

    We describe the magnetic phase of SU(N) $\\mathcal{N}=2$ Super Yang-Mills theories in the self-dual Omega background in terms of a new class of multi-cut matrix models. These arise from a non-perturbative completion of topological strings in the dual four dimensional limit which engineers the gauge theory in the strongly coupled magnetic frame. The corresponding spectral determinants provide natural candidates for the tau functions of isomonodromy problems for flat spectral connections associated to the Seiberg-Witten geometry.

  6. The power of perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Serone, Marco [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Spada, Gabriele [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Villadoro, Giovanni [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy)

    2017-05-10

    We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented.

  7. Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations II: the effect of the transverse mode

    International Nuclear Information System (INIS)

    Tatekawa, Takayuki

    2014-01-01

    We study the initial conditions for cosmological N-body simulations for precision cosmology. In general, Zel'dovich approximation has been applied for the initial conditions of N-body simulations for a long time. These initial conditions provide incorrect higher-order growth. These error caused by setting up the initial conditions by perturbation theory is called transients. We investigated the impact of transient on non-Gaussianity of density field by performing cosmological N-body simulations with initial conditions based on first-, second-, and third-order Lagrangian perturbation theory in previous paper. In this paper, we evaluates the effect of the transverse mode in the third-order Lagrangian perturbation theory for several statistical quantities such as power spectrum and non-Gaussianty. Then we clarified that the effect of the transverse mode in the third-order Lagrangian perturbation theory is quite small

  8. Higher order perturbation theory applied to radiative transfer in non-plane-parallel media

    International Nuclear Information System (INIS)

    Box, M.A.; Polonsky, I.N.; Davis, A.B.

    2003-01-01

    Radiative transfer in non-plane-parallel media is a very challenging problem, which is currently the subject of concerted efforts to develop computational techniques which may be used to tackle different tasks. In this paper we develop the full formalism for another technique, based on radiative perturbation theory. With this approach, one starts with a plane-parallel 'base model', for which many solution techniques exist, and treat the horizontal variability as a perturbation. We show that under the most logical assumption as to the base model, the first-order perturbation term is zero for domain-average radiation quantities, so that it is necessary to go to higher order terms. This requires the computation of the Green's function. While this task is by no means simple, once the various pieces have been assembled they may be re-used for any number of perturbations--that is, any horizontal variations

  9. Very high order lattice perturbation theory for Wilson loops

    International Nuclear Information System (INIS)

    Horsley, R.

    2010-10-01

    We calculate perturbativeWilson loops of various sizes up to loop order n=20 at different lattice sizes for pure plaquette and tree-level improved Symanzik gauge theories using the technique of Numerical Stochastic Perturbation Theory. This allows us to investigate the behavior of the perturbative series at high orders. We observe differences in the behavior of perturbative coefficients as a function of the loop order. Up to n=20 we do not see evidence for the often assumed factorial growth of the coefficients. Based on the observed behavior we sum this series in a model with hypergeometric functions. Alternatively we estimate the series in boosted perturbation theory. Subtracting the estimated perturbative series for the average plaquette from the non-perturbative Monte Carlo result we estimate the gluon condensate. (orig.)

  10. On the non-linear scale of cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-04-15

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  11. On the non-linear scale of cosmological perturbation theory

    International Nuclear Information System (INIS)

    Blas, Diego; Garny, Mathias; Konstandin, Thomas

    2013-04-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  12. On the non-linear scale of cosmological perturbation theory

    CERN Document Server

    Blas, Diego; Konstandin, Thomas

    2013-01-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  13. Evolution of curvature perturbation in generalized gravity theories

    International Nuclear Information System (INIS)

    Matsuda, Tomohiro

    2009-01-01

    Using the cosmological perturbation theory in terms of the δN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy-momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Horava-Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy-momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.

  14. Scalar Quantum Electrodynamics: Perturbation Theory and Beyond

    International Nuclear Information System (INIS)

    Bashir, A.; Gutierrez-Guerrero, L. X.; Concha-Sanchez, Y.

    2006-01-01

    In this article, we calculate scalar propagator in arbitrary dimensions and gauge and the three-point scalar-photon vertex in arbitrary dimensions and Feynman gauge, both at the one loop level. We also discuss constraints on their non perturbative structure imposed by requirements of gauge invariance and perturbation theory

  15. Developments in perturbation theory

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators

  16. Effective field theory of statistical anisotropies for primordial bispectrum and gravitational waves

    Energy Technology Data Exchange (ETDEWEB)

    Rostami, Tahereh; Karami, Asieh; Firouzjahi, Hassan, E-mail: t.rostami@ipm.ir, E-mail: karami@ipm.ir, E-mail: firouz@ipm.ir [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

    2017-06-01

    We present the effective field theory studies of primordial statistical anisotropies in models of anisotropic inflation. The general action in unitary gauge is presented to calculate the leading interactions between the gauge field fluctuations, the curvature perturbations and the tensor perturbations. The anisotropies in scalar power spectrum and bispectrum are calculated and the dependence of these anisotropies to EFT couplings are presented. In addition, we calculate the statistical anisotropy in tensor power spectrum and the scalar-tensor cross correlation. Our EFT approach incorporates anisotropies generated in models with non-trivial speed for the gauge field fluctuations and sound speed for scalar perturbations such as in DBI inflation.

  17. Statistical mechanical perturbation theory of solid-vapor interfacial free energy

    NARCIS (Netherlands)

    Kalikmanov, Vitalij Iosifovitsj; Hagmeijer, Rob; Venner, Cornelis H.

    2017-01-01

    The solid–vapor interfacial free energy γsv plays an important role in a number of physical phenomena, such as adsorption, wetting, and adhesion. We propose a closed form expression for the orientation averaged value of this quantity using a statistical mechanical perturbation approach developed in

  18. Statistical Mechanical Perturbation Theory of Solid−Vapor Interfacial Free Energy

    NARCIS (Netherlands)

    Kalikmanov, V.I.; Hagmeijer, R.; Venner, C.H.

    2017-01-01

    The solid–vapor interfacial free energy γsv plays an important role in a number of physical phenomena, such as adsorption, wetting, and adhesion. We propose a closed form expression for the orientation averaged value of this quantity using a statistical mechanical perturbation approach developed in

  19. Quasilocal quark models as effective theory of non-perturbative QCD

    International Nuclear Information System (INIS)

    Andrianov, A.A.

    2006-01-01

    We consider the Quasilocal Quark Model of NJL type (QNJLM) as effective theory of non-perturbative QCD including scalar (S), pseudo-scalar (P), vector (V) and axial-vector (A) four-fermion interaction with derivatives. In the presence of a strong attraction in the scalar channel the chiral symmetry is spontaneously broken and as a consequence the composite meson states are generated in all channels. With the help of Operator Product Expansion the appropriate set of Chiral Symmetry Restoration (CSR) Sum Rules in these channels are imposed as matching rules to QCD at intermediate energies. The mass spectrum and some decay constants for ground and excited meson states are calculated

  20. Perturbation theory for continuous stochastic equations

    International Nuclear Information System (INIS)

    Chechetkin, V.R.; Lutovinov, V.S.

    1987-01-01

    The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

  1. Chiral perturbation theory

    International Nuclear Information System (INIS)

    Ecker, G.

    1996-06-01

    After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion-pion scattering to two-loop accuracy. In the pion-nucleon system, the linear σ model is contrasted with chiral perturbation theory. The heavy-nucleon expansion is used to construct the effective pion-nucleon Lagrangian to third order in the low-energy expansion, with applications to nucleon Compton scattering. (author)

  2. Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

    International Nuclear Information System (INIS)

    Hanada, Masanori; Matsuura, So; Sugino, Fumihiko

    2012-01-01

    In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N=2U(k) SYM on R 2 ×(Fuzzy R 2 ) around the minimum of k-coincident fuzzy spheres.

  3. In what sense the canonical perturbation theory is gauge-invariant

    International Nuclear Information System (INIS)

    Chen, C.Y.

    1992-07-01

    It is shown that the time-dependent canonical perturbation theory in classical mechanics has unsatisfactory features when dealing with electromagnetic perturbed fields (the perturbed vector potential A-tilde ≠ 0). As a numerical apparatus, the theory relates to gauge-dependent vectors larger than expected. As an analytic apparatus, the theory is involved in unphysical concepts and yields inherently non-gauge-invariant formalisms. By defining the root cause of the problem, an alternative approach is accordingly introduced. (author). 8 refs, 2 figs

  4. Non-perturbative supersymmetry anomaly in supersymmetric QCD

    International Nuclear Information System (INIS)

    Shamir, Y.

    1991-03-01

    The zero modes of the Dirac operator in an instanton and other topologically non-trivial backgrounds are unstable in a large class of massless or partially massless supersymmetric gauge theories. We show that under a generic perturbation of the scalar fields all zero modes become resonances, and discuss the ensuing breakdown of conventional perturbation theory. As a result, despite of the presence of massless fermions, the field theoretic tunneling amplitude is not suppressed. In massless supersymmetric QCD with N c ≤ N f the effective potential is found to be negative and monotonically increasing in the weak coupling regime for scalar VEVs which lie on the perturbatively flat directions. Consequently, massless supersymmetric QCD with N c ≤ N f exhibits a non-perturbative supersymmetry anomaly and exists in a strongly interacting phase which closely resembles ordinary QCD. The same conclusions apply if small masses are added to the lagrangian and the massless limit is smooth. (author). 21 refs, 5 figs

  5. Nonperturbative perturbation theory

    International Nuclear Information System (INIS)

    Bender, C.M.

    1989-01-01

    In this talk we describe a recently proposed graphical perturbative calculational scheme for quantum field theory. The basic idea is to expand in the power of the interaction term. For example, to solve a λφ 4 theory in d-dimensional space-time, we introduce a small parameter δ and consider a λ(φ 2 ) 1+δ field theory. We show how to expand such a theory as a series in powers of δ. The resulting perturbation series appears to have a finite radius of convergence and numerical results for low-dimensional models are good. We have computed the two-point and four-point Green's functions to second order in powers of δ and the 2n-point Green's functions (n>2) to order δ. We explain how to renormalize the theory and show that, to first order in powers of δ, when δ>0 and d≥4 the theory is free. This conclusion remains valid to second order in powers of δ, and we believe that it remains valid to all orders in powers of δ. The new perturbative scheme is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

  6. Perturbation Theory of Embedded Eigenvalues

    DEFF Research Database (Denmark)

    Engelmann, Matthias

    project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...... of dilations is thereby replaced by the unitary group generated y the conjugate operator. This then allows to treat the perturbation problem with the usual Kato theory.......We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...

  7. Non-perturbative description of quantum systems

    CERN Document Server

    Feranchuk, Ilya; Le, Van-Hoang; Ulyanenkov, Alexander

    2015-01-01

    This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory.  In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

  8. The accuracy of QCD perturbation theory at high energies

    CERN Document Server

    Dalla Brida, Mattia; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer

    2016-01-01

    We discuss the determination of the strong coupling $\\alpha_\\mathrm{\\overline{MS}}^{}(m_\\mathrm{Z})$ or equivalently the QCD $\\Lambda$-parameter. Its determination requires the use of perturbation theory in $\\alpha_s(\\mu)$ in some scheme, $s$, and at some energy scale $\\mu$. The higher the scale $\\mu$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $\\Lambda$-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to $\\alpha_s = 0.1$ and below. We find that perturbation theory is very accurate there, yielding a three percent error in the $\\Lambda$-parameter, while data around $\\alpha_s \\approx 0.2$ is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

  9. Non-Perturbative Quantum Geometry III

    CERN Document Server

    Krefl, Daniel

    2016-08-02

    The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.

  10. Thermal gluons beyond pure perturbation theory

    International Nuclear Information System (INIS)

    Reinbach, J.

    2000-01-01

    The perturbative treatment of non-abelian gauge theory at high temperature leads to a threshold in calculation because of chromomagnetic effects. Infinitely many terms of the same order of magnitude arise. The numerical series to be summed is contained in the part of the theory reduced on 3D, which was recently treated non-perturbative as 2+1D Yang-Mills theory at T=0 by Karabali, Kim and Nair. In the thesis in question the exact 3D results are combined with the thermal 4D diagrammatic. In particular the splitting of the space-part of the transverse self-energy in the static limit is treated. As expected, the 3D subsystem can separate as regularized 3D Yang-Mills theory from the 4D structure. In 1-loop order the regulators are received explicit. For 2-loop order it can be shown amongst other things, that the generic contribution with hard inner momenta vanishes. It is examined, how the magnetic mass could follow. Under pressure it is possible to separate the 3D part in 1- and 2-loop order and to receive regulators [de

  11. Non-perturbative renormalization of the chromo-magnetic operator in heavy quark effective theory and the B{sup *} - B mass splitting

    Energy Technology Data Exchange (ETDEWEB)

    Guazzini, D.; Sommer, R. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Meyer, H. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics

    2007-05-15

    We carry out the non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B mesons. We obtain its two-loop anomalous dimension in a Schroedinger functional scheme by successive oneloop conversions to the lattice MS scheme and the MS scheme. We then compute the scale evolution of the operator non-perturbatively in the N{sub f}=0 theory between {mu} {approx}0.3 GeV and {mu} {approx}100 GeV, where contact is made with perturbation theory. The overall renormalization factor that converts the bare lattice operator to its renormalization group invariant form is given for the Wilson gauge action and two standard discretizations of the heavy-quark action. As an application, we find that this factor brings the previous quenched predictions of the B{sup *}-B mass splitting closer to the experimental value than found with a perturbative renormalization. The same renormalization factor is applicable to the spin-dependent potentials of Eichten and Feinberg. (orig.)

  12. Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter

    OpenAIRE

    Harz, Julia; Petraki, Kalliopi

    2018-01-01

    We compute the cross-sections for the radiative capture of non-relativistic particles into bound states, in unbroken perturbative non-Abelian theories. We find that the formation of bound states via emission of a gauge boson can be significant for a variety of dark matter models that feature non-Abelian long-range interactions, including multi-TeV scale WIMPs and dark matter co-annihilating with coloured partners. Our results disagree with previous computations, on the relative sign of the Ab...

  13. Non-perturbative renormalization of HQET and QCD

    International Nuclear Information System (INIS)

    Sommer, Rainer

    2003-01-01

    We discuss the necessity of non-perturbative renormalization in QCD and HQET and explain the general strategy for solving this problem. A few selected topics are discussed in some detail, namely the importance of off shell improvement in the MOM-scheme on the lattice, recent progress in the implementation of finite volume schemes and then particular emphasis is put on the recent idea to carry out a non-perturbative renormalization of the Heavy Quark Effective Theory (HQET)

  14. A stochastic perturbation theory for non-autonomous systems

    Energy Technology Data Exchange (ETDEWEB)

    Moon, W., E-mail: wm275@damtp.cam.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Wettlaufer, J. S., E-mail: wettlaufer@maths.ox.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)

    2013-12-15

    We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.

  15. M-momentum transfer between gravitons, membranes, and fivebranes as perturbative gauge theory processes

    International Nuclear Information System (INIS)

    Keski-Vakkuri, E.; Kraus, P.

    1998-01-01

    Polchinski and Pouliot have shown that M-momentum transfer between membranes in supergravity can be understood as a non-perturbative instanton effect in gauge theory. Here we consider a dual process: electric flux transmission between D-branes. We show that this process can be described in perturbation theory as virtual string pair creation, and is closely related to Schwinger's treatment of the pair creation of charged particles in a uniform electric field. Through the application of dualities, our perturbative calculation gives results for various non-perturbative amplitudes, including M-momentum transfer between gravitons, membranes and longitudinal fivebranes. Thus perturbation theory plus dualities are sufficient to demonstrate agreement between supergravity and gauge theory for a number of M-momentum transferring processes. A variety of other processes where branes are transmitted between branes, e.g. (p,q)-string transmission in IIB theory, can also be studied. We discuss the implications of our results for proving the eleven-dimensional Lorentz invariance of matrix theory. (orig.)

  16. G-fluxes and non-perturbative stabilisation of heterotic M-theory

    International Nuclear Information System (INIS)

    Curio, Gottfried; Krause, Axel

    2002-01-01

    We examine heterotic M-theory compactified on a Calabi-Yau manifold with an additional parallel M5-brane. The dominant non-perturbative effect stems from open membrane instantons connecting the M5 with the boundaries. We derive the four-dimensional low-energy supergravity potential for this situation including subleading contributions as it turns out that the leading term vanishes after minimisation. At the minimum of the potential the M5 gets stabilised at the middle of the orbifold interval while the vacuum energy is shown to be manifestly positive. Moreover, induced by the non-trivial running of the Calabi-Yau volume along the orbifold which is driven by the G-fluxes, we find that the orbifold-length and the Calabi-Yau volume modulus are stabilised at values which are related by the G-flux of the visible boundary. Finally we determine the supersymmetry-breaking scale and the gravitino mass for this open membrane vacuum

  17. Perturbative Quantum Gravity and its Relation to Gauge Theory

    Directory of Open Access Journals (Sweden)

    Bern Zvi

    2002-01-01

    Full Text Available In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on $D$-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input thegravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.

  18. Non-perturbative materialization of ghosts

    International Nuclear Information System (INIS)

    Emparan, Roberto; Garriga, Jaume

    2006-01-01

    In theories with a hidden ghost sector that couples to visible matter through gravity only, empty space can decay into ghosts and ordinary matter by graviton exchange. Perturbatively, such processes can be very slow provided that the gravity sector violates Lorentz invariance above some cut-off scale. Here, we investigate non-perturbative decay processes involving ghosts, such as the spontaneous creation of self-gravitating lumps of ghost matter, as well as pairs of Bondi dipoles (i.e. lumps of ghost matter chasing after positive energy objects). We find the corresponding instantons and calculate their Euclidean action. In some cases, the instantons induce topology change or have negative Euclidean action. To shed some light on the meaning of such peculiarities, we also consider the nucleation of concentrical domain walls of ordinary and ghost matter, where the Euclidean calculation can be compared with the canonical (Lorentzian) description of tunneling. We conclude that non-perturbative ghost nucleation processes can be safely suppressed in phenomenological scenarios

  19. Hybrid perturbation methods based on statistical time series models

    Science.gov (United States)

    San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

    2016-04-01

    In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

  20. Spectral zeta function and non-perturbative effects in ABJM Fermi-gas

    International Nuclear Information System (INIS)

    Hatsuda, Yasuyuki

    2015-03-01

    The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of ''non-perturbative'' poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.

  1. Perturbation theory in light-cone gauge

    International Nuclear Information System (INIS)

    Vianello, Eliana

    2000-01-01

    Perturbation calculations are presented for the light-cone gauge Schwinger model. Eigenstates can be calculated perturbatively but the perturbation theory is nonstandard. We hope to extend the work to QCD 2 to resolve some outstanding issues in those theories

  2. New Variant of the Universal Constants in the Perturbed Chain-Statistical Associating Fluid Theory Equation of State

    DEFF Research Database (Denmark)

    Liang, Xiaodong; Kontogeorgis, Georgios

    2015-01-01

    The Perturbed Chain-Statistical Associating Fluid Theory Equation of State (PC-SAFT EOS) has been successfully applied to model phase behavior of various types of systems, while it is also well-known that the PC-SAFT EOS has difficulties in describing some second-order derivative properties...... resolved the mostly criticized numerical pitfall, that is, the presence of more than three volume roots at real application conditions. Finally, the possibility of using the original PC-SAFT EOS parameters with the new universal constants has been investigated for the phase equilibria of the systems...

  3. Perturbation theory and coupling constant analyticity in two-dimensional field theories

    International Nuclear Information System (INIS)

    Simon, B.

    1973-01-01

    Conjectural material and results over a year old are presented in the discussion of perturbation theory and coupling constant analyticity in two-dimensional field theories. General properties of perturbation series are discussed rather than questions of field theory. The question is interesting for two reasons: First, one would like to understand why perturbation theory is such a good guide (to show that perturbation theory determines the theory in some way). Secondly, one hopes to prove that some or all of the theories are nontrivial. (U.S.)

  4. Extended multi-configuration quasi-degenerate perturbation theory: the new approach to multi-state multi-reference perturbation theory.

    Science.gov (United States)

    Granovsky, Alexander A

    2011-06-07

    The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 1(1)A(')-2(1)A(') conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 1(1)A(1) to 2(1)A(1) electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems. © 2011 American Institute of Physics

  5. Importance of Plasma Response to Non-axisymmetric Perturbations in Tokamaks

    International Nuclear Information System (INIS)

    Park, Jong-kyu; Boozer, Allen H.; Menard, Jonathan E.; Garofalo, Andrea M.; Schaffer, Michael J.; Hawryluk, Richard J.; Kaye, Stanley M.; Gerhardt, Stefan P.; Sabbagh, Steve A. and the NSTX Team

    2009-01-01

    Tokamaks are sensitive to deviations from axisymmetry as small as (delta)B/B 0 ∼ 10 -4 . These non-axisymmetric perturbations greatly modify plasma confinement and performance by either destroying magnetic surfaces with subsequent locking or deforming magnetic surfaces with associated non-ambipolar transport. The Ideal Perturbed Equilibrium Code (IPEC) calculates ideal perturbed equilibria and provides important basis for understanding the sensitivity of tokamak plasmas to perturbations. IPEC calculations indicate that the ideal plasma response, or equivalently the effect by ideally perturbed plasma currents, is essential to explain locking experiments on National Spherical Torus eXperiment (NSTX) and DIII-D. The ideal plasma response is also important for Neoclassical Toroidal Viscosity (NTV) in non-ambipolar transport. The consistency between NTV theory and magnetic braking experiments on NSTX and DIII-D can be improved when the variation in the field strength in IPEC is coupled with generalized NTV theory. These plasma response effects will be compared with the previous vacuum superpositions to illustrate the importance. However, plasma response based on ideal perturbed equilibria is still not sufficiently accurate to predict the details of NTV transport, and can be inconsistent when currents associated with a toroidal torque become comparable to ideal perturbed currents

  6. Perturbation theory around the Wess-Zumino-Witten model

    International Nuclear Information System (INIS)

    Hasseln, H. v.

    1991-05-01

    We consider a perturbation of the Wess-Zumino-Witten model in 2D by a current-current interaction. The β-function is computed to third order in the coupling constant and a nontrivial fixedpoint is found. By non-abelian bosonization, this perturbed WZW-model is shown to have the same β-function (at least to order g 2 ) as the fermionic theory with a four-fermion interaction. (orig.) [de

  7. The use of perturbation theory in density-functional theory

    International Nuclear Information System (INIS)

    Goerling, A.

    1996-01-01

    Perturbation theory with respect to the electron-electron interaction leads to expressions for the exchange and correlation energies and potentials in terms of Kohn-Sham orbitals and Kohn-Sham eigenvalues. An exact open-quote exchange-only close-quote procedure for solids is introduced. Results for several semiconductors are presented. Perturbation theory expansions for the hardness of molecules and the bad gap of solids are given. Density-functional exchange and correlation energies for excited states are defined and a perturbation theory based Kohn-Sham formalism to treat excited states within density-functional theory is introduced

  8. Generalized chiral perturbation theory

    International Nuclear Information System (INIS)

    Knecht, M.; Stern, J.

    1994-01-01

    The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT (Chiral Perturbation Theory), relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard χPT become possible. Emphasis is put on physical aspects rather than on formal developments of GχPT. (author). 31 refs

  9. The sine-Gordon model and the small κ+ region of light- cone perturbation theory

    International Nuclear Information System (INIS)

    Griffin, P.A.

    1992-01-01

    The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the k + = 0 region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non- perturbative β 2 = 8π critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are k + = 0 diagram in light-cone field theory and are individually finite and non-vanishing for all β, conspire to generate ultraviolet divergences of the light-cone energy density. The k + = 0 region of momentum also contributed to connected Green's functions: the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at k + = 0 are properly included. This analysis shows in a simple way how the k + = 0 region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory

  10. Lattice regularized chiral perturbation theory

    International Nuclear Information System (INIS)

    Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.

    2004-01-01

    Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term

  11. Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

    Science.gov (United States)

    Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G

    2017-12-07

    We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

  12. Continual integral in perturbation theory

    International Nuclear Information System (INIS)

    Slavnov, A.A.

    1975-01-01

    It is shown that all results obtained by means of continual integration within the framework of perturbation theory are completely equivalent to those obtained by the usual diagram technique and are therfore just as rigorous. A rigorous justification is given for the rules for operating with continual integrals in perturbation theory. (author)

  13. Non-perturbative quark mass renormalization

    CERN Document Server

    Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.

    1998-01-01

    We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.

  14. Necessary and sufficient conditions for non-perturbative equivalences of large Nc orbifold gauge theories

    International Nuclear Information System (INIS)

    Kovtun, Pave; Uensal, Mithat; Yaffe, Laurence G.

    2005-01-01

    Large N coherent state methods are used to study the relation between U(N c ) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N c limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N c dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N c dynamics of the daughter theory, restricted to the untwisted sector invariant under 'theory space' permutations, coincide. This implies equality, in the large N c limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N c equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N c equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling

  15. The applications of Complexity Theory and Tsallis Non-extensive Statistics at Solar Plasma Dynamics

    Science.gov (United States)

    Pavlos, George

    2015-04-01

    As the solar plasma lives far from equilibrium it is an excellent laboratory for testing complexity theory and non-equilibrium statistical mechanics. In this study, we present the highlights of complexity theory and Tsallis non extensive statistical mechanics as concerns their applications at solar plasma dynamics, especially at sunspot, solar flare and solar wind phenomena. Generally, when a physical system is driven far from equilibrium states some novel characteristics can be observed related to the nonlinear character of dynamics. Generally, the nonlinearity in space plasma dynamics can generate intermittent turbulence with the typical characteristics of the anomalous diffusion process and strange topologies of stochastic space plasma fields (velocity and magnetic fields) caused by the strange dynamics and strange kinetics (Zaslavsky, 2002). In addition, according to Zelenyi and Milovanov (2004) the complex character of the space plasma system includes the existence of non-equilibrium (quasi)-stationary states (NESS) having the topology of a percolating fractal set. The stabilization of a system near the NESS is perceived as a transition into a turbulent state determined by self-organization processes. The long-range correlation effects manifest themselves as a strange non-Gaussian behavior of kinetic processes near the NESS plasma state. The complex character of space plasma can also be described by the non-extensive statistical thermodynamics pioneered by Tsallis, which offers a consistent and effective theoretical framework, based on a generalization of Boltzmann - Gibbs (BG) entropy, to describe far from equilibrium nonlinear complex dynamics (Tsallis, 2009). In a series of recent papers, the hypothesis of Tsallis non-extensive statistics in magnetosphere, sunspot dynamics, solar flares, solar wind and space plasma in general, was tested and verified (Karakatsanis et al., 2013; Pavlos et al., 2014; 2015). Our study includes the analysis of solar plasma time

  16. Non-perturbative aspects of nonlinear sigma models

    Energy Technology Data Exchange (ETDEWEB)

    Flore, Raphael

    2012-12-07

    The aim of this thesis was the study and further development of non-perturbative methods of quantum field theory by means of their application to nonlinear sigma models. While a large part of the physical phenomena of quantum field theory can be successfully predicted by the perturbation theory, some aspects in the region of large coupling strengths are not definitively understood and require suited non-perturbative methods for its analysis. This thesis is concentrated on two approaches, the numerical treatment of field theories on discrete space-time lattices and the functional renormalization group (FRG) as description of the renormalization flux of effective actions. Considerations of the nonlinear O(N) models have shown that for the correct analysis of the critical properties in the framework of the FRG an approach must be chosen, which contained fourth-derivation orders. For this a covariant formalism was developed, which is based on a background-field expansion and the development of a heat kernel. Apart from a destabilizing coupling the results suggest a nontrivial fixed point and by this a non-perturbative renormalizability of these models. The resulting flow diagrams were finally still compared with the results of a numerical analysis of the renormalization flow by means of the Monte-Carlo renormalization group, and hereby qualitative agreement was found. Furthermore an alternative formulation of the FRG in phase-space coordinates was studied and their consistency tested on simple examples. Beyond this an alternative expansion of the effective action in orders of the canonical momenta was applied to the nonlinear O(N) models with the result of a stable non-trivial fixed point, the critical properties of which however show not the expected N-dependence. By means of the FRG finally still the renormalization of topological operators was studied by means of the winding number of the O(3){approx_equal}CP{sup 1} model. By the generalization of the topological

  17. Non-perturbative aspects of nonlinear sigma models

    International Nuclear Information System (INIS)

    Flore, Raphael

    2012-01-01

    The aim of this thesis was the study and further development of non-perturbative methods of quantum field theory by means of their application to nonlinear sigma models. While a large part of the physical phenomena of quantum field theory can be successfully predicted by the perturbation theory, some aspects in the region of large coupling strengths are not definitively understood and require suited non-perturbative methods for its analysis. This thesis is concentrated on two approaches, the numerical treatment of field theories on discrete space-time lattices and the functional renormalization group (FRG) as description of the renormalization flux of effective actions. Considerations of the nonlinear O(N) models have shown that for the correct analysis of the critical properties in the framework of the FRG an approach must be chosen, which contained fourth-derivation orders. For this a covariant formalism was developed, which is based on a background-field expansion and the development of a heat kernel. Apart from a destabilizing coupling the results suggest a nontrivial fixed point and by this a non-perturbative renormalizability of these models. The resulting flow diagrams were finally still compared with the results of a numerical analysis of the renormalization flow by means of the Monte-Carlo renormalization group, and hereby qualitative agreement was found. Furthermore an alternative formulation of the FRG in phase-space coordinates was studied and their consistency tested on simple examples. Beyond this an alternative expansion of the effective action in orders of the canonical momenta was applied to the nonlinear O(N) models with the result of a stable non-trivial fixed point, the critical properties of which however show not the expected N-dependence. By means of the FRG finally still the renormalization of topological operators was studied by means of the winding number of the O(3)≅CP 1 model. By the generalization of the topological operator and the

  18. Off-critical statistical models: factorized scattering theories and bootstrap program

    International Nuclear Information System (INIS)

    Mussardo, G.

    1992-01-01

    We analyze those integrable statistical systems which originate from some relevant perturbations of the minimal models of conformal field theories. When only massive excitations are present, the systems can be efficiently characterized in terms of the relativistic scattering data. We review the general properties of the factorizable S-matrix in two dimensions with particular emphasis on the bootstrap principle. The classification program of the allowed spins of conserved currents and of the non-degenerate S-matrices is discussed and illustrated by means of some significant examples. The scattering theories of several massive perturbations of the minimal models are fully discussed. Among them are the Ising model, the tricritical Ising model, the Potts models, the series of the non-unitary minimal models M 2,2n+3 , the non-unitary model M 3,5 and the scaling limit of the polymer system. The ultraviolet limit of these massive integrable theories can be exploited by the thermodynamics Bethe ansatz, in particular the central charge of the original conformal theories can be recovered from the scattering data. We also consider the numerical method based on the so-called conformal space truncated approach which confirms the theoretical results and allows a direct measurement of the scattering data, i.e. the masses and the S-matrix of the particles in bootstrap interaction. The problem of computing the off-critical correlation functions is discussed in terms of the form-factor approach

  19. Wilson loops to 20th order numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Hotzel, G.; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Ilgenfritz, E.M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Joint Institute for Nuclear Research, VBLHEP, Dubna (Russian Federation); Millo, R.; Rakow, P.E.L. [Liverpool Univ. (Germany). Theoretical Physics Div.; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe, Hyogo (Japan); Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2012-05-15

    We calculate Wilson loops of various sizes up to 20 loops in SU(3) pure lattice gauge theory at different lattice sizes for Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high loop orders. We observe differences in the behavior of those series as function of the loop order. Up to n=20 we do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. Alternatively we estimate the total series in boosted perturbation theory using information from the first 14 loops. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their non-perturbative parts.

  20. Supersymmetry restoration in superstring perturbation theory

    International Nuclear Information System (INIS)

    Sen, Ashoke

    2015-01-01

    Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.

  1. Supersymmetry restoration in superstring perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Sen, Ashoke [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India)

    2015-12-14

    Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.

  2. Non-perturbative QCD. Renormalization, O(a)-improvement and matching to heavy quark effective theory

    Energy Technology Data Exchange (ETDEWEB)

    Sommer, R.

    2006-11-15

    We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed directly to an overview of the literature and our personal assessment of what has been achieved and what is missing. II. The computation of the running coupling, running quark masses and the extraction of the renormalization group invariants. We focus on the basic strategy and on the large effort that has been invested in understanding the continuum limit. We point out what remains to be done. III. Non-perturbative Heavy Quark Effective Theory. Since the literature on this subject is still rather sparse, we go beyond the basic ideas and discuss in some detail how the theory works in principle and in practice. (orig.)

  3. Non-perturbative QCD. Renormalization, O(a)-improvement and matching to heavy quark effective theory

    International Nuclear Information System (INIS)

    Sommer, R.

    2006-11-01

    We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed directly to an overview of the literature and our personal assessment of what has been achieved and what is missing. II. The computation of the running coupling, running quark masses and the extraction of the renormalization group invariants. We focus on the basic strategy and on the large effort that has been invested in understanding the continuum limit. We point out what remains to be done. III. Non-perturbative Heavy Quark Effective Theory. Since the literature on this subject is still rather sparse, we go beyond the basic ideas and discuss in some detail how the theory works in principle and in practice. (orig.)

  4. Operator Decomposition Framework for Perturbation Theory

    Energy Technology Data Exchange (ETDEWEB)

    Abdel-Khalik, Hany S.; Wang, Congjian; Bang, Young Suk [North Carolina State University, Raleigh (United States)

    2012-05-15

    This summary describes a new framework for perturbation theory intended to improve its performance, in terms of the associated computational cost and the complexity of implementation, for routine reactor calculations in support of design, analysis, and regulation. Since its first introduction in reactor analysis by Winger, perturbation theory has assumed an aura of sophistication with regard to its implementation and its capabilities. Only few reactor physicists, typically mathematically proficient, have contributed to its development, with the general body of the nuclear engineering community remaining unaware of its current status, capabilities, and challenges. Given its perceived sophistication and the small body of community users, the application of perturbation theory has been limited to investigatory analyses only. It is safe to say that the nuclear community is split into two groups, a small one which understands the theory and, and a much bigger group with the perceived notion that perturbation theory is nothing but a fancy mathematical approach that has very little use in practice. Over the past three years, research has demonstrated two goals. First, reduce the computational cost of perturbation theory in order to enable its use for routine reactor calculations. Second, expose some of the myth about perturbation theory and present it in a form that is simple and relatable in order to stimulate the interest of nuclear practitioners, especially those who are currently working on the development of next generation reactor design and analysis tools. The operator decomposition approach has its roots in linear algebra and can be easily understood by code developers, especially those involved in the design of iterative numerical solution strategies

  5. Instantons and large N an introduction to non-perturbative methods in quantum field theory

    CERN Document Server

    Marino, Marcos

    2015-01-01

    This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang-Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behaviour of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.

  6. Analysis of self-consistency effects in range-separated density-functional theory with Møller-Plesset perturbation theory

    DEFF Research Database (Denmark)

    Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard

    2011-01-01

    Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled......-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using Møller-Plesset-type (MP......) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational...

  7. Some phenomenological consequences of the time-ordered perturbation theory of QED on non-commutative spacetime

    CERN Document Server

    Liao, Y

    2003-01-01

    A framework was recently proposed for doing perturbation theory on non-commutative (NC) spacetime. It preserves the unitarity of the S matrix and differs from the naive, popular approach already at the lowest order in perturbation when time does not commute with space. In this work, we investigate its phenomenological implications at linear colliders, especially the TESLA at DESY, through the processes of e sup + e sup --> mu sup +mu sup - ,H sup + H sup - ,H sup 0 H sup 0. We find that some NC effects computed previously are now modified and that there are new processes which now exhibit NC effects. Indeed, the first two processes get corrected at tree level as opposed to the null result in the naive approach, while the third one coincides with the naive result only in the low energy limit. The impact of the earth's rotation is incorporated. The NC signals are generally significant when the NC scale is comparable to the collider energy. If this is not the case, the non-trivial azimuthal angle distribution an...

  8. 't Hooft loops and perturbation theory

    CERN Document Server

    De Forcrand, Philippe; Noth, D; Forcrand, Philippe de; Lucini, Biagio; Noth, David

    2005-01-01

    We show that high-temperature perturbation theory describes extremely well the area law of SU(N) spatial 't Hooft loops, or equivalently the tension of the interface between different Z_N vacua in the deconfined phase. For SU(2), the disagreement between Monte Carlo data and lattice perturbation theory for sigma(T)/T^2 is less than 2%, down to temperatures O(10) T_c. For SU(N), N>3, the ratios of interface tensions, (sigma_k/sigma_1)(T), agree with perturbation theory, which predicts tiny deviations from the ratio of Casimirs, down to nearly T_c. In contrast, individual tensions differ markedly from the perturbative expression. In all cases, the required precision Monte Carlo measurements are made possible by a simple but powerful modification of the 'snake' algorithm.

  9. Non-perturbative power corrections to ghost and gluon propagators

    International Nuclear Information System (INIS)

    Boucaud, Philippe; Leroy, Jean-Pierre; Yaouanc, Alain Le; Lokhov, Alexey; Micheli, Jacques; Pene, Olivier; RodrIguez-Quintero, Jose; Roiesnel, Claude

    2006-01-01

    We study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ( ≅ 270MeV) of Λ M-barS-bar than the one obtained from the propagators separately( ≅ 320MeV). This argues in favour of significant non-perturbative ∼ 1/q 2 power corrections in the ghost and gluon propagators. We check the self-consistency of the method

  10. Coupling-parameter expansion in thermodynamic perturbation theory.

    Science.gov (United States)

    Ramana, A Sai Venkata; Menon, S V G

    2013-02-01

    An approach to the coupling-parameter expansion in the liquid state theory of simple fluids is presented by combining the ideas of thermodynamic perturbation theory and integral equation theories. This hybrid scheme avoids the problems of the latter in the two phase region. A method to compute the perturbation series to any arbitrary order is developed and applied to square well fluids. Apart from the Helmholtz free energy, the method also gives the radial distribution function and the direct correlation function of the perturbed system. The theory is applied for square well fluids of variable ranges and compared with simulation data. While the convergence of perturbation series and the overall performance of the theory is good, improvements are needed for potentials with shorter ranges. Possible directions for further developments in the coupling-parameter expansion are indicated.

  11. Non-perturbative topological strings and conformal blocks

    NARCIS (Netherlands)

    Cheng, M.C.N.; Dijkgraaf, R.; Vafa, C.

    2011-01-01

    We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to

  12. Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism

    CERN Document Server

    Blas, Diego; Ivanov, Mikhail M.; Sibiryakov, Sergey

    2016-01-01

    We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein--de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This pave...

  13. Perturbative spacetimes from Yang-Mills theory

    Energy Technology Data Exchange (ETDEWEB)

    Luna, Andrés [School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Monteiro, Ricardo [Theoretical Physics Department, CERN,Geneva (Switzerland); Nicholson, Isobel; Ochirov, Alexander; O’Connell, Donal [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Westerberg, Niclas [Institute of Photonics and Quantum Sciences,School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh (United Kingdom); Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); White, Chris D. [Centre for Research in String Theory,School of Physics and Astronomy, Queen Mary University of London,327 Mile End Road, London E1 4NS (United Kingdom)

    2017-04-12

    The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.

  14. Perturbation theory for arbitrary coupling strength?

    Science.gov (United States)

    Mahapatra, Bimal P.; Pradhan, Noubihary

    2018-03-01

    We present a new formulation of perturbation theory for quantum systems, designated here as: “mean field perturbation theory” (MFPT), which is free from power-series-expansion in any physical parameter, including the coupling strength. Its application is thereby extended to deal with interactions of arbitrary strength and to compute system-properties having non-analytic dependence on the coupling, thus overcoming the primary limitations of the “standard formulation of perturbation theory” (SFPT). MFPT is defined by developing perturbation about a chosen input Hamiltonian, which is exactly solvable but which acquires the nonlinearity and the analytic structure (in the coupling strength) of the original interaction through a self-consistent, feedback mechanism. We demonstrate Borel-summability of MFPT for the case of the quartic- and sextic-anharmonic oscillators and the quartic double-well oscillator (QDWO) by obtaining uniformly accurate results for the ground state of the above systems for arbitrary physical values of the coupling strength. The results obtained for the QDWO may be of particular significance since “renormalon”-free, unambiguous results are achieved for its spectrum in contrast to the well-known failure of SFPT in this case.

  15. Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

    International Nuclear Information System (INIS)

    Zhang Zhijie; Jiang Dongguang; Wang Wei

    2011-01-01

    Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)

  16. Quasi-Chemical PC-SAFT: An Extended Perturbed Chain-Statistical Associating Fluid Theory for Lattice-Fluid Mixtures.

    Science.gov (United States)

    Parvaneh, Khalil; Shariati, Alireza

    2017-09-07

    In this study, a new modification of the perturbed chain-statistical associating fluid theory (PC-SAFT) has been proposed by incorporating the lattice fluid theory of Guggenheim as an additional term to the original PC-SAFT terms. As the proposed model has one more term than the PC-SAFT, a new mixing rule has been developed especially for the new additional term, while for the conventional terms of the PC-SAFT, the one-fluid mixing rule is used. In order to evaluate the proposed model, the vapor-liquid equilibria were estimated for binary CO 2 mixtures with 16 different ionic liquids (ILs) of the 1-alkyl-3-methylimidazolium family with various anions consisting of bis(trifluoromethylsulfonyl) imide, hexafluorophosphate, tetrafluoroborate, and trifluoromethanesulfonate. For a comprehensive comparison, three different modes (different adjustable parameters) of the proposed model were compared with the conventional PC-SAFT. Results indicate that the proposed modification of the PC-SAFT EoS is generally more reliable with respect to the conventional PC-SAFT in all the three proposed modes of vapor-liquid equilibria, giving good agreement with literature data.

  17. Random surfaces: A non-perturbative regularization of strings?

    International Nuclear Information System (INIS)

    Ambjoern, J.

    1989-12-01

    I review the basic properties of the theory of randum surfaces. While it is by now well known that the theory of (discretized) random surfaces correctly describes the (perturbative) aspects of non-critical strings in d 1. In these lectures I intend to show that the theory of dynamical triangulated random surfaces provides us with a lot of information about the dynamics of both the bosonic string and the superstring even for d>1. I also briefly review recent attempts to define a string field theory (sum over all genus) in this approach. (orig.)

  18. Non-perturbative improvement of stout-smeared three flavour clover fermions

    Energy Technology Data Exchange (ETDEWEB)

    Cundy, N.; Goeckeler, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (GB). School of Physics and Astronomy] (and others)

    2009-01-15

    We discuss a 3-flavour lattice QCD action with clover improvement in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree-level) Symanzik improved gluon action this constitutes the Stout Link Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover term coefficient has to be tuned. We present here results of a non-perturbative determination of this coefficient using the Schroedinger functional and as a by-product a determination of the critical hopping parameter. Comparisons of the results are made with lowest order perturbation theory. (orig.)

  19. Higher order perturbation theory - An example for discussion

    International Nuclear Information System (INIS)

    Lewins, J.D.; Parks, G.; Babb, A.L.

    1986-01-01

    Higher order perturbation theory is developed in the form of a Taylor series expansion to third order to calculate the thermal utilization of a nonuniform cell. The development takes advantage of the self-adjoint property of the diffusion operator to provide a simple development of this illustration of generalized perturbation theory employing scalar perturbation parameters. The results show how a designer might employ a second-order theory to quantify proposed design improvements, together with the limitations of second- and third-order theory. The chosen example has an exact optimization solution and thus provides a clear understanding of the role of perturbation theory at its various orders. Convergence and the computational advantages and disadvantages of the method are discussed

  20. Non-Gaussianity from inflation: theory and observations

    Science.gov (United States)

    Bartolo, N.; Komatsu, E.; Matarrese, S.; Riotto, A.

    2004-11-01

    This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provide all the tools necessary to compute at second order in perturbation theory the level of non-Gaussianity in any model of cosmological perturbations. We discuss the new wave of models of inflation, which are firmly rooted in modern particle physics theory and predict a significant amount of non-Gaussianity. The review is addressed to both astrophysicists and particle physicists and contains useful tables which summarize the theoretical and observational results regarding non-Gaussianity.

  1. Non perturbative aspects of strongly correlated electron systems

    International Nuclear Information System (INIS)

    Controzzi, D.

    2000-01-01

    In this thesis we report some selected works on Strongly Correlated Electron Systems. A common ingredient of these works is the use of non-perturbative techniques available in low dimensions. In the first part we use the Bethe Ansatz to study some properties of two families of integrable models introduced by Fateev. We calculate the Thermodynamics of the models and show how they can be interpreted as effective Landau-Ginzburg theories for coupled two-dimensional superconductors interacting with an insulating substrate. This allows us to study exactly the dependence of the critical temperature on the thickness of the insulating layer, and on the interaction between the order parameters of two different superconducting planes. In the second part of the thesis we study the optical conductivity of the sine-Gordon model using the Form Factor method and Conformal Perturbation Theory. This allows us to develop, for the first time, a complete theory of the optical conductivity of one-dimensional Mott insulators, in the Quantum Field Theory limit. (author)

  2. Instantaneous stochastic perturbation theory

    International Nuclear Information System (INIS)

    Lüscher, Martin

    2015-01-01

    A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.

  3. Generalized perturbation theory using two-dimensional, discrete ordinates transport theory

    International Nuclear Information System (INIS)

    Childs, R.L.

    1979-01-01

    Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions

  4. Higgs phase in non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Kaymakcalan, O.S.

    1981-06-01

    A non-Abelian gauge theory involving scalar fields with non-tachyonic mass terms in the Lagrangian is considered, in order to construct a finite energy density trial vacuum for this theory. The usual scalar potential arguments suggest that the vacuum of such a theory would be in the perturbative phase. However, the obvious choices for a vacuum in this phase, the Axial gauge and the Coulomb gauge bare vacua, do not have finite energy densities even with an ultraviolet cutoff. Indeed, it is a non-trivial problem to construct finite energy density vacua for non-Abelian gauge theories and this is intimately connected with the gauge fixing degeneracies of these theories. Since the gauge fixing is achieved in the Unitary gauge, this suggests that the Unitary gauge bare vacuum might be a finite energy trial vacuum and, despite the form of the scalar potential, the vacuum of this theory might be in a Higgs phase rather than the perturbative phase

  5. Time-sliced perturbation theory for large scale structure I: general formalism

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego; Garny, Mathias; Sibiryakov, Sergey [Theory Division, CERN, CH-1211 Genève 23 (Switzerland); Ivanov, Mikhail M., E-mail: diego.blas@cern.ch, E-mail: mathias.garny@cern.ch, E-mail: mikhail.ivanov@cern.ch, E-mail: sergey.sibiryakov@cern.ch [FSB/ITP/LPPC, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland)

    2016-07-01

    We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.

  6. Perturbation-induced emergence of Poisson-like behavior in non-Poisson systems

    International Nuclear Information System (INIS)

    Akin, Osman C; Grigolini, Paolo; Paradisi, Paolo

    2009-01-01

    The response of a system with ON–OFF intermittency to an external harmonic perturbation is discussed. ON–OFF intermittency is described by means of a sequence of random events, i.e., the transitions from the ON to the OFF state and vice versa. The unperturbed waiting times (WTs) between two events are assumed to satisfy a renewal condition, i.e., the WTs are statistically independent random variables. The response of a renewal model with non-Poisson ON–OFF intermittency, associated with non-exponential WT distribution, is analyzed by looking at the changes induced in the WT statistical distribution by the harmonic perturbation. The scaling properties are also studied by means of diffusion entropy analysis. It is found that, in the range of fast and relatively strong perturbation, the non-Poisson system displays a Poisson-like behavior in both WT distribution and scaling. In particular, the histogram of perturbed WTs becomes a sequence of equally spaced peaks, with intensity decaying exponentially in time. Further, the diffusion entropy detects an ordinary scaling (related to normal diffusion) instead of the expected unperturbed anomalous scaling related to the inverse power-law decay. Thus, an analysis based on the WT histogram and/or on scaling methods has to be considered with some care when dealing with perturbed intermittent systems

  7. Perturbation Theory of the Cosmological Log-Density Field

    DEFF Research Database (Denmark)

    Wang, Xin; Neyrinck, Mark; Szapudi, István

    2011-01-01

    , motivating an analytic study of it. In this paper, we develop cosmological perturbation theory for the power spectrum of this field. Our formalism is developed in the context of renormalized perturbation theory, which helps to regulate the convergence behavior of the perturbation series, and of the Taylor...

  8. Perturbation theory and collision probability formalism. Vol. 2

    Energy Technology Data Exchange (ETDEWEB)

    Nasr, M [National Center for Nuclear Safety and Radiation Control, Atomic Energy Authority, Cairo (Egypt)

    1996-03-01

    Perturbation theory is commonly used in evaluating the activity effects, particularly those resulting from small and localized perturbation in multiplying media., e.g. in small sample reactivity measurements. The Boltzmann integral transport equation is generally used for evaluating the direct and adjoint fluxes in the heterogenous lattice cells to be used in the perturbation equations. When applying perturbation theory in this formalism, a term involving the perturbation effects on the special transfer kernel arises. This term is difficult to evaluate correctly, since it involves an integration all over the entire system. The main advantage of the perturbation theory which is the limitation of the integration procedure on the perturbation region is found to be of no practical use in such cases. In the present work, the perturbation equation in the collision probability formalism is analyzed. A mathematical treatment of the term in question is performed. A new mathematical expression for this term is derived. The new expression which can be estimated easily is derived.

  9. Multiphoton transitions in semiconductors in the non-perturbative approach

    International Nuclear Information System (INIS)

    Iqbal, M.Z.; Hassan, A.R.

    1987-09-01

    Transition rates for multiphoton absorption via direct band-to-band excitation have been calculated using a non-perturbative approach due to Jones and Reiss, based on the Volkov type final state wave functions. Both cases of parabolic and non-parabolic energy bands have been included in our calculations. Absorption coefficients have been obtained for the cases of plane polarized and circularly polarized light. In particular, two-photon absorption coefficients are derived for the two cases of polarization for the parabolic band approximation as well as for non-parabolic bands and compared with the results based on perturbation theory. Numerical estimates of the two photon absorption coefficients resulting from our calculations are also provided. (author). 10 refs, 1 tab

  10. Non-perturbative Heavy-Flavor Transport at RHIC and LHC

    Energy Technology Data Exchange (ETDEWEB)

    He, Min, E-mail: mhe@comp.tamu.edu; Fries, Rainer J.; Rapp, Ralf

    2013-08-15

    We calculate open heavy-flavor (HF) transport in relativistic heavy-ion collisions by applying a strong-coupling treatment in both macro- and microscopic dynamics (hydrodynamics and non-perturbative diffusion interactions). The hydrodynamic medium evolution is quantitatively constrained by bulk and multi-strange hadron spectra and elliptic flow. The heavy quark transport coefficient is evaluated from a non-perturbative T-matrix approach in the Quark–Gluon Plasma which, close to the critical temperature, leads to resonance formation and feeds into the recombination of heavy quarks on a hydrodynamic hypersurface. In the hadronic phase, the diffusion of HF mesons is obtained from effective hadronic theory. We compute observables at RHIC and LHC for non-photonic electrons and HF mesons, respectively.

  11. String perturbation theory diverges

    International Nuclear Information System (INIS)

    Gross, D.J.; Periwal, V.

    1988-01-01

    We prove that perturbation theory for the bosonic string diverges for arbitrary values of the coupling constant and is not Borel summable. This divergence is independent of the existence of the infinities that occur in the theory due to the presence of tachyons and dilaton tadpoles. We discuss the physical implications of such a divergence

  12. Non-Gaussianity at tree and one-loop levels from vector field perturbations

    International Nuclear Information System (INIS)

    Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon; Lyth, David H.

    2009-01-01

    We study the spectrum P ζ and bispectrum B ζ of the primordial curvature perturbation ζ when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree-level terms [both (either) in P ζ and (or) in B ζ ] and vice versa. The level of non-Gaussianity in the bispectrum, f NL , is calculated and related to the level of statistical anisotropy in the power spectrum, g ζ . For very small amounts of statistical anisotropy in the power spectrum, the level of non-Gaussianity may be very high, in some cases exceeding the current observational limit.

  13. Discrete state perturbation theory via Green's functions

    International Nuclear Information System (INIS)

    Rubinson, W.

    1975-01-01

    The exposition of stationary-state perturbation theory via the Green's function method in Goldberger and Watson's Collision Theory is reworked in a way that makes explicit its mathematical basis. It is stressed that the theory consists of the construction of, and manipulations on, a mathematical identity. The perturbation series fall out of the identity almost immediately. The logical status of the method is commented on

  14. A non-perturbative definition of 2D quantum gravity by the fifth time action

    International Nuclear Information System (INIS)

    Ambjoern, J.; Greensite, J.; Varsted, S.

    1990-07-01

    The general formalism for stabilizing bottomless Euclidean field theories (the 'fifth-time' action) provides a natural non-perturbative definition of matrix models corresponding to 2d quantum gravity. The formalism allows, in principle, the use of lattice Monte Carlo techniques for non-perturbative computation of correlation functions. (orig.)

  15. Perturbations and quasi-normal modes of black holes in Einstein-Aether theory

    International Nuclear Information System (INIS)

    Konoplya, R.A.; Zhidenko, A.

    2007-01-01

    We develop a new method for calculation of quasi-normal modes of black holes, when the effective potential, which governs black hole perturbations, is known only numerically in some region near the black hole. This method can be applied to perturbations of a wide class of numerical black hole solutions. We apply it to the black holes in the Einstein-Aether theory, a theory where general relativity is coupled to a unit time-like vector field, in order to observe local Lorentz symmetry violation. We found that in the non-reduced Einstein-Aether theory, real oscillation frequency and damping rate of quasi-normal modes are larger than those of Schwarzschild black holes in the Einstein theory

  16. Effective field theory of cosmological perturbations

    International Nuclear Information System (INIS)

    Piazza, Federico; Vernizzi, Filippo

    2013-01-01

    The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu–Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy. (paper)

  17. Effective field theory of cosmological perturbations

    Science.gov (United States)

    Piazza, Federico; Vernizzi, Filippo

    2013-11-01

    The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.

  18. Four-fluxes and non-perturbative superpotentials in two dimensions

    International Nuclear Information System (INIS)

    Lerche, W.

    1998-01-01

    We show how certain non-perturbative superpotentials W(Σ), which are the two-dimensional analogs of the Seiberg-Witten prepotential in 4d, can be computed via geometric engineering from 4-folds. We analyze an explicit example for which the relevant compact geometry of the 4-fold is given by P 1 fibered over P 2 . In the field theory limit, this gives an effective U(1) gauge theory with N=(2,2) supersymmetry in two dimensions. We find that the analog of the SW curve is a K3 surface, and that the complex FI coupling is given by the modular parameter of this surface. The FI potential itself coincides with the middle period of a meromorphic differential. However, it only shows up in the effective action if a certain 4-flux is switched on, and then supersymmetry appears to be non-perturbatively broken. (orig.)

  19. Cosmological Perturbation Theory Using the Schrödinger Equation

    Science.gov (United States)

    Szapudi, István; Kaiser, Nick

    2003-01-01

    We introduce the theory of nonlinear cosmological perturbations using the correspondence limit of the Schrödinger equation. The resulting formalism is equivalent to using the collisionless Boltzmann (or Vlasov) equations, which remain valid during the whole evolution, even after shell crossing. Other formulations of perturbation theory explicitly break down at shell crossing, e.g., Eulerean perturbation theory, which describes gravitational collapse in the fluid limit. This Letter lays the groundwork by introducing the new formalism, calculating the perturbation theory kernels that form the basis of all subsequent calculations. We also establish the connection with conventional perturbation theories, by showing that third-order tree-level results, such as bispectrum, skewness, cumulant correlators, and three-point function, are exactly reproduced in the appropriate expansion of our results. We explicitly show that cumulants up to N=5 predicted by Eulerian perturbation theory for the dark matter field δ are exactly recovered in the corresponding limit. A logarithmic mapping of the field naturally arises in the Schrödinger context, which means that tree-level perturbation theory translates into (possibly incomplete) loop corrections for the conventional perturbation theory. We show that the first loop correction for the variance is σ2=σ2L+(-1.14- n)σ4L for a field with spectral index n. This yields 1.86 and 0.86 for n=-3 and -2, respectively, to be compared with the exact loop order corrections 1.82 and 0.88. Thus, our tree-level theory recovers the dominant part of first-order loop corrections of the conventional theory, while including (partial) loop corrections to infinite order in terms of δ.

  20. A simple extrapolation of thermodynamic perturbation theory to infinite order

    International Nuclear Information System (INIS)

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2015-01-01

    Recent analyses of the third and fourth order perturbation contributions to the equations of state for square well spheres and Lennard-Jones chains show trends that persist across orders and molecular models. In particular, the ratio between orders (e.g., A 3 /A 2 , where A i is the ith order perturbation contribution) exhibits a peak when plotted with respect to density. The trend resembles a Gaussian curve with the peak near the critical density. This observation can form the basis for a simple recursion and extrapolation from the highest available order to infinite order. The resulting extrapolation is analytic and therefore cannot fully characterize the critical region, but it remarkably improves accuracy, especially for the binodal curve. Whereas a second order theory is typically accurate for the binodal at temperatures within 90% of the critical temperature, the extrapolated result is accurate to within 99% of the critical temperature. In addition to square well spheres and Lennard-Jones chains, we demonstrate how the method can be applied semi-empirically to the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT)

  1. Non-perturbative background field calculations

    International Nuclear Information System (INIS)

    Stephens, C.R.; Department of Physics, University of Utah, Salt Lake City, Utah 84112)

    1988-01-01

    New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation: perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation. copyright 1988 Academic Press, Inc

  2. Non-perturbative background field calculations

    Science.gov (United States)

    Stephens, C. R.

    1988-01-01

    New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

  3. Cosmological perturbations in theories with non-minimal coupling between curvature and matter

    International Nuclear Information System (INIS)

    Bertolami, Orfeu; Frazão, Pedro; Páramos, Jorge

    2013-01-01

    In this work, we examine how the presence of a non-minimal coupling between spacetime curvature and matter affects the evolution of cosmological perturbations on a homogeneous and isotropic Universe, and hence the formation of large-scale structure. This framework places constraints on the terms which arise due to the coupling with matter and, in particular, on the modified growth of matter density perturbations. We derive approximate analytical solutions for the evolution of matter overdensities during the matter dominated era and discuss the compatibility of the obtained results with the hypothesis that the late time acceleration of the Universe is driven by a non-minimal coupling

  4. Fermi interaction. Conservation of vector current and modified perturbation theory

    International Nuclear Information System (INIS)

    Rochev, V.E.

    1983-01-01

    The Fermi interaction (anti psi ysub(n) psi)sup(2) is investigated with the method of auxilary field. The analogues of the Ward-Takahashi electrodynamical identities and the gauge transformations of Green functions, that are the consequence of the conservation of vector current, have been obtained. The gauge function for the spinor propagator is the exponential superpropagator. The arguments are given in favour of the existence of a modified perturbation theory, which is finite in every order and non-analytical over its coupling constant, for the four-fermion interaction. The non-analytical part is defined unambiguously, and the analytical part contains a set of finite dimensionless constants to define which non-perturbative information is needed. The simplest model (the chain approximation) for the non-stable vector bound state is considered

  5. Perturbative anyon gas

    International Nuclear Information System (INIS)

    Dasnieres de Veigy, A.; Ouvry, S.; Paris-6 Univ., 75

    1992-06-01

    The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant α is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a 3 , a 4 , a 5 and a 6 are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs

  6. 1/4 BPS States and Non-Perturbative Couplings in N=4 String Theories

    CERN Document Server

    Lerche, W.

    1999-01-01

    We compute certain 2K+4-point one-loop couplings in the type IIA string compactified on K3 x T^2, which are related a topological index on this manifold. Their special feature is that they are sensitive to only short and intermediate BPS multiplets. The couplings derive from underlying prepotentials of the form G(T,U)=d^{2K}V ln[chi10(T,U,V)], where chi10(T,U,V) is the helicity partition function of 1/4 BPS states. In the dual heterotic string on T^6, the amplitudes describe non-perturbative gravitational corrections due to bound states of fivebrane instantons with heterotic world-sheet instantons. We argue, as a consequence, that our results give information about instanton configurations in six dimensional Sp(2k) gauge theories on T^6.

  7. Non-perturbative subtractions in the heavy quark effective field theory

    International Nuclear Information System (INIS)

    Maiani, L.; Martinelli, G.; Sachrajda, C.T.

    1992-01-01

    We demonstrate the presence of ultraviolet power divergences in the O(1/m h ) corrections to matrix elements of hadronic operators containing a heavy quark field (where m h is the mass of the heavy quark). These power divergences must be subtracted non-perturbatively. The implications for lattice computations are discussed in detail. (orig.)

  8. Driven similarity renormalization group: Third-order multireference perturbation theory.

    Science.gov (United States)

    Li, Chenyang; Evangelista, Francesco A

    2017-03-28

    A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6 ) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2 , H 2 O 2 , C 2 H 6 , and N 2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST =E T -E S ) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol -1 , a value that is within 0.1 kcal mol -1 from multireference coupled cluster results.

  9. Communication: Random phase approximation renormalized many-body perturbation theory

    International Nuclear Information System (INIS)

    Bates, Jefferson E.; Furche, Filipp

    2013-01-01

    We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations

  10. The theory of singular perturbations

    CERN Document Server

    De Jager, E M

    1996-01-01

    The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat

  11. Controlling quark mass determinations non-perturbatively in three-flavour QCD

    CERN Document Server

    Campos, Isabel

    2017-01-01

    The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS-bar scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf=3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.

  12. Application of linear and higher perturbation theory in reactor physics

    International Nuclear Information System (INIS)

    Woerner, D.

    1978-01-01

    For small perturbations in the material composition of a reactor according to the first approximation of perturbation theory the eigenvalue perturbation is proportional to the perturbation of the system. This assumption is true for the neutron flux not influenced by the perturbance. The two-dimensional code LINESTO developed for such problems in this paper on the basis of diffusion theory determines the relative change of the multiplication constant. For perturbations varying the neutron flux in the space of energy and position the eigenvalue perturbation is also influenced by this changed neutron flux. In such cases linear perturbation theory yields larger errors. Starting from the methods of calculus of variations there is additionally developed in this paper a perturbation method of calculation permitting in a quick and simple manner to assess the influence of flux perturbation on the eigenvalue perturbation. While the source of perturbations is evaluated in isotropic approximation of diffusion theory the associated inhomogeneous equation may be used to determine the flux perturbation by means of diffusion or transport theory. Possibilities of application and limitations of this method are studied in further systematic investigations on local perturbations. It is shown that with the integrated code system developed in this paper a number of local perturbations may be checked requiring little computing time. With it flux perturbations in first approximation and perturbations of the multiplication constant in second approximation can be evaluated. (orig./RW) [de

  13. Superfield perturbation theory and renormalization

    International Nuclear Information System (INIS)

    Delbourgo, R.

    1975-01-01

    The perturbation theory graphs and divergences in super-symmetric Lagrangian models are studied by using superfield techniques. In super PHI 3 -theory very little effort is needed to arrive at the single infinite (wave function) renormalization counterterm, while in PHI 4 -theory the method indicates the counter-Lagrangians needed at the one-loop level and possibly beyond

  14. Massive states in chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Mallik, S [Saha Inst. of Nuclear Physics, Calcutta (India)

    1995-08-01

    It is shown that the chiral nonanalytic terms generated by {Delta}{sub 33} resonance in the nucleon self-energy is reproduced in chiral perturbation theory by perturbing appropriate local operators contained in the pion-nucleon effective Lagrangian itself. (orig.)

  15. A non-perturbative argument for the non-abelian Higgs mechanism

    International Nuclear Information System (INIS)

    De Palma, G.; Strocchi, F.

    2013-01-01

    The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion

  16. A non-perturbative argument for the non-abelian Higgs mechanism

    Energy Technology Data Exchange (ETDEWEB)

    De Palma, G. [Scuola Normale Superiore, Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy); Strocchi, F., E-mail: franco.strocchi@sns.it [INFN, Sezione di Pisa, Pisa (Italy)

    2013-09-15

    The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion.

  17. Holomorphic couplings in non-perturbative string compactifications

    International Nuclear Information System (INIS)

    Klevers, Denis Marco

    2011-06-01

    In this thesis we present an analysis of several aspects of four-dimensional, non-perturbative N = 1 compactifications of string theory. Our focus is on the study of brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N=1 effective action, most prominently the superpotential W. The thesis is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we demonstrate exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefold Z 3 , that is canonically constructed from the original five-brane and Calabi-Yau threefold Z 3 via a blow-up. We exploit the use of the blow-up threefold Z 3 as a tool to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpret Z 3 as a flux compactification dual to the original five-brane by defining an SU(3)-structure on Z 3 , that is generated dynamically by the five-brane backreaction. (orig.)

  18. Determination of the QCD Λ-parameter and the accuracy of perturbation theory at high energies

    International Nuclear Information System (INIS)

    Dalla Brida, Mattia; Fritzsch, Patrick; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer; Humboldt-Universitaet, Berlin

    2016-04-01

    We discuss the determination of the strong coupling α_M_S(m_Z) or equivalently the QCD Λ-parameter. Its determination requires the use of perturbation theory in α_s(μ) in some scheme, s, and at some energy scale μ. The higher the scale μ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to α_s=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a three percent error in the Λ-parameter, while data around α_s∼0.2 is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

  19. Determination of the QCD Λ-parameter and the accuracy of perturbation theory at high energies

    Energy Technology Data Exchange (ETDEWEB)

    Dalla Brida, Mattia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Fritzsch, Patrick [Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM/CSIC; Korzec, Tomasz [Wuppertal Univ. (Germany). Dept. of Physics; Ramos, Alberto [CERN - European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Collaboration: ALPHA Collaboration

    2016-04-15

    We discuss the determination of the strong coupling α{sub MS}(m{sub Z}) or equivalently the QCD Λ-parameter. Its determination requires the use of perturbation theory in α{sub s}(μ) in some scheme, s, and at some energy scale μ. The higher the scale μ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to α{sub s}=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a three percent error in the Λ-parameter, while data around α{sub s}∼0.2 is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

  20. New Approaches and Applications for Monte Carlo Perturbation Theory

    Energy Technology Data Exchange (ETDEWEB)

    Aufiero, Manuele; Bidaud, Adrien; Kotlyar, Dan; Leppänen, Jaakko; Palmiotti, Giuseppe; Salvatores, Massimo; Sen, Sonat; Shwageraus, Eugene; Fratoni, Massimiliano

    2017-02-01

    This paper presents some of the recent and new advancements in the extension of Monte Carlo Perturbation Theory methodologies and application. In particular, the discussed problems involve Brunup calculation, perturbation calculation based on continuous energy functions, and Monte Carlo Perturbation Theory in loosely coupled systems.

  1. Elliptic CY3folds and non-perturbative modular transformation

    International Nuclear Information System (INIS)

    Iqbal, Amer; Shabbir, Khurram

    2016-01-01

    We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections. (orig.)

  2. Elliptic CY3folds and non-perturbative modular transformation

    Energy Technology Data Exchange (ETDEWEB)

    Iqbal, Amer [Government College University, Abdus Salam School of Mathematical Sciences, Lahore (Pakistan); Shabbir, Khurram [Government College University, Department of Mathematics, Lahore (Pakistan)

    2016-03-15

    We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections. (orig.)

  3. Perturbation theory from stochastic quantization

    International Nuclear Information System (INIS)

    Hueffel, H.

    1984-01-01

    By using a diagrammatical method it is shown that in scalar theories the stochastic quantization method of Parisi and Wu gives the usual perturbation series in Feynman diagrams. It is further explained how to apply the diagrammatical method to gauge theories, discussing the origin of ghost effects. (Author)

  4. Closed form bound-state perturbation theory

    Directory of Open Access Journals (Sweden)

    Ollie J. Rose

    1980-01-01

    Full Text Available The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.

  5. Homological Perturbation Theory for Nonperturbative Integrals

    Science.gov (United States)

    Johnson-Freyd, Theo

    2015-11-01

    We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In particular, we explain that phenomena usually thought of as particular to asymptotic integrals in fact also occur exactly: integrals of the type appearing in quantum field theory can be reduced in a totally algebraic fashion to integrals over an Euler-Lagrange locus, provided this locus is understood in the scheme-theoretic sense, so that imaginary critical points and multiplicities of degenerate critical points contribute.

  6. Similarity-transformed perturbation theory on top of truncated local coupled cluster solutions: Theory and applications to intermolecular interactions

    Energy Technology Data Exchange (ETDEWEB)

    Azar, Richard Julian, E-mail: julianazar2323@berkeley.edu; Head-Gordon, Martin, E-mail: mhg@cchem.berkeley.edu [Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

    2015-05-28

    Your correspondents develop and apply fully nonorthogonal, local-reference perturbation theories describing non-covalent interactions. Our formulations are based on a Löwdin partitioning of the similarity-transformed Hamiltonian into a zeroth-order intramonomer piece (taking local CCSD solutions as its zeroth-order eigenfunction) plus a first-order piece coupling the fragments. If considerations are limited to a single molecule, the proposed intermolecular similarity-transformed perturbation theory represents a frozen-orbital variant of the “(2)”-type theories shown to be competitive with CCSD(T) and of similar cost if all terms are retained. Different restrictions on the zeroth- and first-order amplitudes are explored in the context of large-computation tractability and elucidation of non-local effects in the space of singles and doubles. To accurately approximate CCSD intermolecular interaction energies, a quadratically growing number of variables must be included at zeroth-order.

  7. Numerical stochastic perturbation theory in the Schroedinger functional

    International Nuclear Information System (INIS)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Dalla Brida, Mattia; Sint, Stefan; Deutsches Elektronen-Synchrotron

    2013-11-01

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  8. Numerical stochastic perturbation theory in the Schroedinger functional

    Energy Technology Data Exchange (ETDEWEB)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2013-11-15

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  9. Non-gaussianity from the trispectrum and vector field perturbations

    International Nuclear Information System (INIS)

    Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon

    2010-01-01

    We use the δN formalism to study the trispectrum T ζ of the primordial curvature perturbation ζ when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, τ NL , is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f NL , and the level of statistical anisotropy in the power spectrum, g ζ . Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on τ NL from WMAP, for generic inflationary models, is done.

  10. Quasi-degenerate perturbation theory using matrix product states

    International Nuclear Information System (INIS)

    Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

    2016-01-01

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost

  11. Quasi-degenerate perturbation theory using matrix product states

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, Sandeep, E-mail: sanshar@gmail.com; Jeanmairet, Guillaume [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Alavi, Ali, E-mail: a.alavi@fkf.mpg.de [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)

    2016-01-21

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

  12. Quasi-degenerate perturbation theory using matrix product states

    Science.gov (United States)

    Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

    2016-01-01

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

  13. Statistical mechanics of lattice Boson field theory

    International Nuclear Information System (INIS)

    1976-01-01

    A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3 and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region

  14. Statistical mechanics of lattice boson field theory

    International Nuclear Information System (INIS)

    Baker, G.A. Jr.

    1977-01-01

    A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3, and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region. 24 references

  15. A primer for chiral perturbation theory

    CERN Document Server

    Scherer, Stefan

    2012-01-01

    Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques.

  16. Holomorphic couplings in non-perturbative string compactifications

    Energy Technology Data Exchange (ETDEWEB)

    Klevers, Denis Marco

    2011-06-15

    In this thesis we present an analysis of several aspects of four-dimensional, non-perturbative N = 1 compactifications of string theory. Our focus is on the study of brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N=1 effective action, most prominently the superpotential W. The thesis is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we demonstrate exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefold Z{sub 3}, that is canonically constructed from the original five-brane and Calabi-Yau threefold Z{sub 3} via a blow-up. We exploit the use of the blow-up threefold Z{sub 3} as a tool to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpret Z{sub 3} as a flux compactification dual to the original five-brane by defining an SU(3)-structure on Z{sub 3}, that is generated dynamically by the five-brane backreaction. (orig.)

  17. Infrared problems in field perturbation theory

    International Nuclear Information System (INIS)

    David, Francois.

    1982-12-01

    The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr

  18. Multiple-Trace Operators and Non-Local String Theories

    International Nuclear Information System (INIS)

    Silverstein, Eva M.

    2001-01-01

    We propose that a novel deformation of string perturbation theory, involving non-local interactions between strings, is required to describe the gravity duals of field theories deformed by multiple-trace operators. The new perturbative expansion involves a new parameter, which is neither the string coupling nor the coefficient of a vertex operator on the worldsheet. We explore some of the properties of this deformation, focusing on a special case where the deformation in the field theory is exactly marginal

  19. A Theory of the Podkletnov Effect based on General Relativity: Anti-Gravity Force due to the Perturbed Non-Holonomic Background of Space

    Directory of Open Access Journals (Sweden)

    Rabounski D.

    2007-07-01

    Full Text Available We consider the Podkletnov effect — the weight loss of an object located over a superconducting disc in air due to support by an alternating magnetic field. We consider this problem using the mathematical methods of General Relativity. We show via Einstein’s equations and the geodesic equations in a space perturbed by a disc undergoing oscillatory bounces orthogonal to its own plane, that there is no r ˆ ole of superconductivity; the Podkletnov effect is due to the fact that the field of the background space non-holonomity (the basic non-othogonality of time lines to the spatial section, being perturbed by such an oscillating disc produces energy and momentum flow in order to compensate the perturbation in itself. Such a momentum flow is directed above the disc in Podkletnov’s experiment, so it works like negative gravity (anti-gravity. We propose a simple mechanical system which, simulating the Podkletnov effect, is an experimental test of the whole theory. The theory allows for other “anti-gravity devices”, which simulate the Podkletnov effect without use of very costly superconductor technology. Such devices could be applied to be used as a cheap source of new energy, and could have implications to air and space travel.

  20. Chiral perturbation theory

    International Nuclear Information System (INIS)

    Harada, Masayasu

    2009-01-01

    Chiral perturbation theory has been used for great number of phenomenological analyses in low energy QCD as well as the lattice QCD analyses since the creation of the theory by Weinberg in 1979 followed by its consolidation by Gasser and Leutwyler in 1984 and 85. The theory is now the highly established one as the approach based on the effective field theory to search for Green function including quantum correlations in the frame of the systematic expansion technique using Lagrangian which includes all of the terms allowed by the symmetry. This review has been intended to describe how systematically physical quantities are calculated in the framework of the chiral symmetry. Consequently many of the various phenomenological analyses are not taken up here for which other reports are to be referred. Further views are foreseen to be developed based on the theory in addition to numbers of results reported up to the present. Finally π-π scattering is taken up to discuss to what energy scale the theory is available. (S. Funahashi)

  1. "Phonon" scattering beyond perturbation theory

    Science.gov (United States)

    Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing

    2016-02-01

    Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.

  2. Non-Gaussian Statistical Communication Theory

    CERN Document Server

    Middleton, David

    2012-01-01

    The book is based on the observation that communication is the central operation of discovery in all the sciences. In its "active mode" we use it to "interrogate" the physical world, sending appropriate "signals" and receiving nature's "reply". In the "passive mode" we receive nature's signals directly. Since we never know a prioriwhat particular return signal will be forthcoming, we must necessarily adopt a probabilistic model of communication. This has developed over the approximately seventy years since it's beginning, into a Statistical Communication Theory (or SCT). Here it is the set or

  3. Perturbation theory of the quark-gluon plasma at finite temperature and baryon number density

    International Nuclear Information System (INIS)

    Anon.

    1984-01-01

    At very high energy densities, hadronic matter becomes an almost ideal gas of quarks and gluons. In these circumstances, the effects of particle interactions are small, and to some order in perturbation theory are computable by methods involving weak coupling expansions. To illustrate the perturbative methods which may be used to compute the thermodynamic potential, the results and methods which are employed to compute to first order in α/sub s/ are reviewed. The problem of the plasmon effect, and the necessity of using non-perturbative methods when going beyond first order in α/sub s/ in evaluating the thermodynamic potential are discussed. The results at zero temperature and finite baryon number density to second order in α/sub s/ are also reviewed. The method of renormalization group improving the weak coupling expansions by replacing the expansion by an expansion in a temperature and baryon number density dependent coupling which approaches zero at high energy densities is discussed. Non-perturbative effects such as instantons are briefly mentioned and the breakdown of perturbation theory for the thermodynamical at order α/sub s/ 3 for finite temperature is presented

  4. Basics of QCD perturbation theory

    International Nuclear Information System (INIS)

    Soper, D.E.

    1997-01-01

    This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs

  5. Basics of QCD perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Soper, D.E. [Univ. of Oregon, Eugene, OR (United States). Inst. of Theoretical Science

    1997-06-01

    This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.

  6. A complete non-perturbative renormalization prescription for quasi-PDFs

    Energy Technology Data Exchange (ETDEWEB)

    Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Constantinou, Martha [Temple Univ., Philadelphia, PA (United States). Dept. of Physics; Hadjiyiannakou, Kyriakos [The Cyprus Institute, Nicosia (Cyprus); Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Panagopoulos, Haralambos [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Collaboration: European Twisted Mass Collaboration

    2017-06-15

    In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI{sup '} scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with N{sub f}=2+1+1 dynamical quarks, and a pion mass of around 375 MeV.

  7. Review of chiral perturbation theory

    Indian Academy of Sciences (India)

    Abstract. A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.

  8. A primer for Chiral Perturbative Theory

    International Nuclear Information System (INIS)

    Scherer, Stefan; Schindler, Matthias R.; George Washington Univ., Washington, DC

    2012-01-01

    Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques. (orig.)

  9. Convergent perturbation expansions for Euclidean quantum field theory

    International Nuclear Information System (INIS)

    Mack, G.; Pordt, A.

    1984-09-01

    Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean Quantum Field Theory to arbitrary accuracy, including 'nonperturbative' contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional lambdaphi 4 -theory (in continuous space). They are not essentially more complicated than standard perturbation theory. The n-th order term is expressed in terms of 0(n)-dimensional integrals, and is of order lambda 4 if 4k-3<=n<=4k. (orig.)

  10. Non-gaussianity from the trispectrum and vector field perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Valenzuela-Toledo, Cesar A., E-mail: cavalto@ciencias.uis.edu.c [Escuela de Fisica, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia); Rodriguez, Yeinzon, E-mail: yeinzon.rodriguez@uan.edu.c [Escuela de Fisica, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia); Centro de Investigaciones, Universidad Antonio Narino, Cra 3 Este 47A-15, Bogota D.C. (Colombia)

    2010-03-01

    We use the deltaN formalism to study the trispectrum T{sub z}eta of the primordial curvature perturbation zeta when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, tau{sub NL}, is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f{sub NL}, and the level of statistical anisotropy in the power spectrum, g{sub z}eta. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on tau{sub NL} from WMAP, for generic inflationary models, is done.

  11. Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations

    International Nuclear Information System (INIS)

    Orlenko, E. V.; Evstafev, A. V.; Orlenko, F. E.

    2015-01-01

    A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated

  12. Exact perturbation theory of multiphoton processes at high intensities. [Schroedinger equation, perturbation theory, matrix

    Energy Technology Data Exchange (ETDEWEB)

    Faisal, F H.M. [Bielefeld Univ. (Germany, F.R.). Fakultaet fuer Physik

    1976-06-11

    In this work the perturbation theory for multiphoton processes at high intensities is investigated and it is described an analytical method of summing the perturbation series to extract the contribution from all terms that give rise to the absorption of N photons by an atomic system. The method is first applied to the solution of a simple model problem and the result is confirmed by direct integration of the model Schroedinger equation. The usual lowest (nonvanishing)-order perturbation-theoretical calculation is also carried out for this model to demonstrate explicitly that the full result correctly reproduces that of the lowest-order theory in the limit of low intensity. The method is then extended to the case of an atomic system with well-developed spectrum (e.g. H atom) and the N-photon T-matrix is derived in terms of a ''photon matrix'' asub(N), for which a three-term recurrence relation is established. Next, from the vantage point of the general result obtained here, A probe is made into the nature of several approximate nonperturbative solutions that have appeared in the literature in the past. It is shown here that their applicability is severely restricted by the requirement of the essential spectral degeneracy of the atomic system. Finally, appendix A outlines a prescription of computing the photon matrix asub(N), which (as in the usual lowest-order perturbation-theoretical calculation)requires a knowledge of the eigenfunctions and eigenvalues of the atomic Hamiltonian only.

  13. Non-adiabatic perturbations in multi-component perfect fluids

    Energy Technology Data Exchange (ETDEWEB)

    Koshelev, N.A., E-mail: koshna71@inbox.ru [Ulyanovsk State University, Leo Tolstoy str 42, 432970 (Russian Federation)

    2011-04-01

    The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.

  14. Non-adiabatic perturbations in multi-component perfect fluids

    International Nuclear Information System (INIS)

    Koshelev, N.A.

    2011-01-01

    The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models

  15. Methods and applications of analytical perturbation theory

    International Nuclear Information System (INIS)

    Kirchgraber, U.; Stiefel, E.

    1978-01-01

    This monograph on perturbation theory is based on various courses and lectures held by the authors at the ETH, Zurich and at the University of Texas, Austin. Its principal intention is to inform application-minded mathematicians, physicists and engineers about recent developments in this field. The reader is not assumed to have mathematical knowledge beyond what is presented in standard courses on analysis and linear algebra. Chapter I treats the transformations of systems of differential equations and the integration of perturbed systems in a formal way. These tools are applied in Chapter II to celestial mechanics and to the theory of tops and gyroscopic motion. Chapter III is devoted to the discussion of Hamiltonian systems of differential equations and exposes the algebraic aspects of perturbation theory showing also the necessary modifications of the theory in case of singularities. The last chapter gives the mathematical justification for the methods developed in the previous chapters and investigates important questions such as error estimations for the solutions and asymptotic stability. Each chapter ends with useful comments and an extensive reference to the original literature. (HJ) [de

  16. Perturbation theory and importance functions in integral transport formulations

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Perturbation theory expressions for the static reactivity derived from the flux, collision density, birth-rate density, and fission-neutron density formulations of integral transport theory, and from the integro-differential formulation, are intercompared. The physical meaning and relation of the adjoint functions corresponding to each of the five formulations are established. It is found that the first-order approximation of the perturbation expressions depends on the transport theory formulation and on the adjoint function used. The approximations of the integro-differential formulation corresponding to different first-order approximations of the integral transport theory formulations are identified. It is found that the accuracy of all first-order approximations of the integral transport formulations examined is superior to the accuracy of first-order integro-differential perturbation theory

  17. Where does cosmological perturbation theory break down?

    International Nuclear Information System (INIS)

    Armendariz-Picon, Cristian; Fontanini, Michele; Penco, Riccardo; Trodden, Mark

    2009-01-01

    It is often assumed that initial conditions for the evolution of a cosmological mode should be set at the time its physical wavelength reaches a cut-off of the order of the Planck length. Beyond that scale, trans-Planckian corrections to the dispersion relation are supposed to become dominant, leading to the breakdown of cosmological perturbation theory. In this paper, we apply the effective field theory approach to the coupled metric-inflaton system in order to calculate the corrections to the power spectrum of scalar and tensor perturbations induced by higher-dimension operators at short wavelengths. These corrections can be interpreted as modifications of the dispersion relation, and thus open a window to probe the validity of cosmological perturbation theory. Both for scalars and tensors, the modifications become important when the Hubble parameter is of the order of the Planck mass, or when the physical wave number of a cosmological perturbation mode approaches the square of the Planck mass divided by the Hubble constant. Thus, the cut-off length at which such a breakdown occurs is finite, but much smaller than the Planck length.

  18. Second-order generalized perturbation theory for source-driven systems

    International Nuclear Information System (INIS)

    Greenspan, E.; Gilai, D.; Oblow, E.M.

    1978-01-01

    A second-order generalized perturbation theory (GPT) for the effect of multiple system variations on a general flux functional in source-driven systems is derived. The derivation is based on a functional Taylor series in which second-order derivatives are retained. The resulting formulation accounts for the nonlinear effect of a given variation accurate to third order in the flux and adjoint perturbations. It also accounts for the effect of interaction between any number of variations. The new formulation is compared with exact perturbation theory as well as with perturbation theory for altered systems. The usefulnes of the second-order GPT formulation is illustrated by applying it to optimization problems. Its applicability to areas of cross-section sensitivity analysis and system design and evaluation is also discussed

  19. Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Papinutto, M.; Pena, C. [CERN, Geneva (Switzerland). Physics Dept., Theory Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik

    2007-06-15

    We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of {delta}B=2 parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by nonperturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered. (orig.)

  20. Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Doering, C.R.

    1985-01-01

    Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

  1. The tension as perturbative parameter in string theory

    International Nuclear Information System (INIS)

    Gamboa, J.

    1990-01-01

    We propose an approach to string theory where the zero theory is the null string. We find an explicit form of the propagator for the null string in the momentum space. We show that considering the tension as perturbative parameter, the perturbative series is completely summable and we find the propagator of the bosonic open string with tension T. (author) [pt

  2. Transport perturbation theory in nuclear reactor analysis

    International Nuclear Information System (INIS)

    Nishigori, Takeo; Takeda, Toshikazu; Selvi, S.

    1985-01-01

    Perturbation theory is formulated on the basis of transport theory to obtain a formula for the reactivity changes due to possible variations of cross sections. Useful applications to cell homogenization are presented for the whole core calculation in transport and in diffusion theories. (author)

  3. Testing QCD in the non-perturbative regime

    Energy Technology Data Exchange (ETDEWEB)

    A.W. Thomas

    2007-01-01

    This is an exciting time for strong interaction physics. We have a candidate for a fundamental theory, namely QCD, which has passed all the tests thrown at it in the perturbative regime. In the non-perturbative regime it has also produced some promising results and recently a few triumphs but the next decade will see enormous progress in our ability to unambiguously calculate the consequences of non-perturbative QCD and to test those predictions experimentally. Amongst the new experimental facilities being constructed, the hadronic machines at JPARC and GSI-FAIR and the 12 GeV Upgrade at Jefferson Lab, the major new electromagnetic facility worldwide, present a beautifully complementary network aimed at producing precise new measurements which will advance our knowledge of nuclear systems and push our ability to calculate the consequences of QCD to the limit. We will first outline the plans at Jefferson Lab for doubling the energy of CEBAF. The new facility presents some wonderful opportunities for discovery in strong interaction physics, as well as beyond the standard model. Then we turn to the theoretical developments aimed at extracting precise results for physical hadron properties from lattice QCD simulations. This discussion will begin with classical examples, such as the mass of the nucleon and ?, before dealing with a very recent and spectacular success involving information extracted from modern parity violating electron scattering.

  4. Locally extracting scalar, vector and tensor modes in cosmological perturbation theory

    International Nuclear Information System (INIS)

    Clarkson, Chris; Osano, Bob

    2011-01-01

    Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second and higher order because perturbative modes are sourced by products of lower order modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second order. We perform much of our analysis using an index-free 'vector-calculus' approach which makes manipulating tensor equations considerably simpler. (papers)

  5. Perturbed Chern-Simons theory, fractional statistics, and Yang-Baxter algebra

    International Nuclear Information System (INIS)

    Chatterjee, A.; Sreedhar, V.V.

    1992-01-01

    Topological Chern-Simons theory coupled to matter fields is analysed in the framework of Dirac's method of quantising constrained systems in a general class of linear, non-local gauges. We show that in the weak coupling limit gauge invariant operators in the theory transform under an exchange according to a higher dimensional representation of the braid group which is built out of the fundamental representation matrices of the gauge group and thus behave like anyons. We also discover new solutions of the Yang-Baxter equation which emerges as a consistency condition on the structure functions of the operator algebra of the matter fields. (orig.)

  6. Wilson loops in very high order lattice perturbation theory

    International Nuclear Information System (INIS)

    Ilgenfritz, E.M.; Nakamura, Y.; Perlt, H.; Schiller, A.; Rakow, P.E.L.; Schierholz, G.; Regensburg Univ.

    2009-10-01

    We calculate Wilson loops of various sizes up to loop order n=20 for lattice sizes of L 4 (L=4,6,8,12) using the technique of Numerical Stochastic Perturbation Theory in quenched QCD. This allows to investigate the behaviour of the perturbative series at high orders. We discuss three models to estimate the perturbative series: a renormalon inspired fit, a heuristic fit based on an assumed power-law singularity and boosted perturbation theory. We have found differences in the behavior of the perturbative series for smaller and larger Wilson loops at moderate n. A factorial growth of the coefficients could not be confirmed up to n=20. From Monte Carlo measured plaquette data and our perturbative result we estimate a value of the gluon condensate left angle (α)/(π)GG right angle. (orig.)

  7. Canonical perturbation theory in linearized general relativity theory

    International Nuclear Information System (INIS)

    Gonzales, R.; Pavlenko, Yu.G.

    1986-01-01

    Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field

  8. Perturbative quantum field theory via vertex algebras

    International Nuclear Information System (INIS)

    Hollands, Stefan; Olbermann, Heiner

    2009-01-01

    In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras. Our starting point is the Wilson-Zimmermann operator product expansion (OPE). Following ideas of a previous paper (S. Hollands, e-print arXiv:0802.2198), we consider a consistency (essentially associativity) condition satisfied by the coefficients in this expansion. We observe that the information in the OPE coefficients can be repackaged straightforwardly into 'vertex operators' and that the consistency condition then has essentially the same form as the key condition in the theory of vertex algebras. We develop a general theory of perturbations of the algebras that we encounter, similar in nature to the Hochschild cohomology describing the deformation theory of ordinary algebras. The main part of the paper is devoted to the question how one can calculate the perturbations corresponding to a given interaction Lagrangian (such as λφ 4 ) in practice, using the consistency condition and the corresponding nonlinear field equation. We derive graphical rules, which display the vertex operators (i.e., OPE coefficients) in terms of certain multiple series of hypergeometric type.

  9. Non-perturbative test of the Witten-Veneziano formula from lattice QCD

    International Nuclear Information System (INIS)

    Cichy, Krzysztof; Jansen, Karl; Ottnad, Konstantin; Urbach, Carsten; Bonn Univ.

    2015-10-01

    We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with N f =2 +1+1 dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU(2) chiral limits we compare both sides and find good agreement within uncertainties.

  10. Status of chiral perturbation theory

    International Nuclear Information System (INIS)

    Ecker, G.

    1996-10-01

    A survey is made of semileptonic and nonleptonic kaon decays in the framework of chiral perturbation theory. The emphasis is on what has been done rather than how it was done. The theoretical predictions are compared with available experimental results. (author)

  11. Theory of deep inelastic neutron scattering: Hard-core perturbation theory

    International Nuclear Information System (INIS)

    Silver, R.N.

    1988-01-01

    Details are presented of a new many-body theory for deep inelastic neutron scattering (DINS) experiments to measure momentum distributions in quantum fluids and solids. The high-momentum and energy-transfer scattering law in helium is shown to be a convolution of the impulse approximation with a final-state broadening function which depends on the scattering phase shifts and the radial distribution function. The predicted broadening satisfies approximate Y scaling, is neither Lorentzian nor Gaussian, and obeys the f, ω 2 , and ω 3 sum rules. The derivation uses a combination of Liouville perturbation theory, projection superoperators, and semiclassical methods which I term ''hard-core perturbation theory.'' A review is presented of the predictions of prior theories for DINS experiments in relation to the present work. A subsequent paper will present massive numerical predictions and a discussion of DINS experiments on superfluid 4 He

  12. Interacting fermions in two dimensions: Beyond the perturbation theory

    International Nuclear Information System (INIS)

    Gangadharaiah, S.; Maslov, D.L.; Chubukov, A.V.; Glazman, L.I.

    2005-05-01

    We consider a system of 2D fermions with short-range interaction. A straightforward perturbation theory is shown to be ill-defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. We show that the divergences result from the interaction of fermions with the zero-sound collective mode. By re-summing the most divergent diagrams, we obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. We also show that the interaction with the zero sound does not affect a non- analytic, T 2 -part of the specific heat. (author)

  13. Analysis of observables in Chern-Simons perturbation theory

    International Nuclear Information System (INIS)

    Alvarez, M.; Labastida, J.M.F.

    1993-01-01

    Chern-Simons theory with gauge group SU(N) is analyzed from a perturbation theory point of view. Computations up to order g 6 of the vacuum expectation value of the unknot are carried out and it is shown that agreement with the exact result by Witten implies no quantum correction at two loops for the two-point function. In addition, it is shown from a perturbation theory point of view that the framing dependence of the vacuum expectation value of an arbitrary knot factorizes in the form predicted by Witten. (orig.)

  14. A finite element formulation for perturbation theory calculations

    International Nuclear Information System (INIS)

    Ozgener, B.; Kaluc, S.

    2004-01-01

    Full text: When the introduced change in the configuration of a nuclear system is neutronically not too significant, the use of the perturbation theory approximation ('the perturbation theory method' or PTM) is usually considered as an alternative to the recalculation of the effective multiplication factor (K eff ) of the modified system ('the diffusion theory method' or DTM) for the determination of the ensuing change in reactivity. In the DTM, the change in reactivity due to the introduced change can be calculated by the multigroup diffusion theory by performing two K eff determinations, one for the original and one for the modified system. The accuracy of this method is only limited by the approximations inherent in the multigroup diffusion theory and the numerical method employed for its solution. The error stemming from the numerical approximation can be nearly eliminated by utilizing a fine enough spatial mesh ad an 'exact' solution is nearly possible. Its basic disadvantage relative to the PTM is the necessity of a new K eff calculation for every change in the configuration no matter how small. On the other hand, if we use PTM, with an only one-time calculation of the flux and the adjoint flux of the original system, the change in reactivity due to any kind of perturbation can be approximately calculated using the changes in the cross section data in the perturbation theory reactivity formula. The accuracy of the PTM is restricted by the size and location of the induced change. In this work, our aim is to assess the accuracy of PTM relative to the DTM and determine criteria for the justification of its use. For all required solutions of the normal and adjoint multigroup diffusion equations, we choose the finite element method (FEM) as our numerical method and a 1-D cylindrical geometry model. The underlying theory is implemented in our FORTRAN program PERTURB. The validation of PERTURB is carried out via comparisons with analytical solutions for bare and

  15. Non-perturbative plaquette in 3d pure SU(3)

    CERN Document Server

    Hietanen, A; Laine, Mikko; Rummukainen, K; Schröder, Y

    2005-01-01

    We present a determination of the elementary plaquette and, after the subsequent ultraviolet subtractions, of the finite part of the gluon condensate, in lattice regularization in three-dimensional pure SU(3) gauge theory. Through a change of regularization scheme to MSbar and a matching back to full four-dimensional QCD, this result determines the first non-perturbative contribution in the weak-coupling expansion of hot QCD pressure.

  16. On the domain of string perturbation theory

    International Nuclear Information System (INIS)

    Davis, S.

    1989-06-01

    For a large class of effectively closed surfaces, it is shown that the only divergences in string scattering amplitudes at each order in perturbation theory are those associated with the coincidence of vertex operators and the boundary of moduli space. This class includes all closed surfaces of finite genus, and infinite-genus surfaces which can be uniformized by a group of Schottky type. While the computation is done explicitly for bosonic strings in their ground states, it can also be extended to excited states and to superstrings. The properties of these amplitudes lead to a definition of the domain of perturbation theory as the set of effectively closed surfaces. The implications of the restriction to effectively closed surfaces on the behavior of the perturbation series are discussed. (author). 20 refs, 6 figs

  17. Perturbative Gaussianizing transforms for cosmological fields

    Science.gov (United States)

    Hall, Alex; Mead, Alexander

    2018-01-01

    Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

  18. Strings as perturbations of evolving spin networks

    International Nuclear Information System (INIS)

    Smolin, Lee

    2000-01-01

    One step in the construction of a background independent formulation of string theory is detailed, in which it is shown how perturbative strings may arise as small fluctuations around histories in a formulation of non-perturbative dynamics of spin networks due to Markopoulou. In this formulation the dynamics of spin network states and their generalizations is described in terms of histories which have discrete analogues of the causal structure and many fingered time of Lorentzian spacetimes. Perturbations of these histories turn out to be described in terms of spin systems defined on 2-dimensional timelike surfaces embedded in the discrete spacetime. When the history has a classical limit which is Minkowski spacetime, the action of the perturbation theory is given to leading order by the spacetime area of the surface, as in bosonic string theory. This map between a non-perturbative formulation of quantum gravity and a 1+1 dimensional theory generalizes to a large class of theories in which the group SU(2) i s extended to any quantum group or supergroup. It is argued that a necessary condition for the non-perturbative theory to have a good classical limit is that the resulting 1+1 dimensional theory defines a consistent and stable perturbative string theory

  19. Perturbation theory for water with an associating reference fluid

    Science.gov (United States)

    Marshall, Bennett D.

    2017-11-01

    The theoretical description of the thermodynamics of water is challenged by the structural transition towards tetrahedral symmetry at ambient conditions. As perturbation theories typically assume a spherically symmetric reference fluid, they are incapable of accurately describing the liquid properties of water at ambient conditions. In this paper we address this problem by introducing the concept of an associated reference perturbation theory (APT). In APT we treat the reference fluid as an associating hard sphere fluid which transitions to tetrahedral symmetry in the fully hydrogen bonded limit. We calculate this transition in a theoretically self-consistent manner without appealing to molecular simulations. This associated reference provides the reference fluid for a second order Barker-Henderson perturbative treatment of the long-range attractions. We demonstrate that this approach gives a significantly improved description of water as compared to standard perturbation theories.

  20. Scattering theory of space-time non-commutative abelian gauge field theory

    International Nuclear Information System (INIS)

    Rim, Chaiho; Yee, Jaehyung

    2005-01-01

    The unitary S-matrix for space-time non-commutative quantum electrodynamics is constructed using the *-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, we formulate the perturbation theory and present the Feynman rule. We then apply this perturbation analysis to the Compton scattering process to the lowest order and check the gauge invariance of the scattering amplitude at this order.

  1. Non-perturbative Debye mass in finite-T QCD

    CERN Document Server

    Kajantie, Keijo; Peisa, J; Rajantie, A; Rummukainen, K; Shaposhnikov, Mikhail E

    1997-01-01

    Employing a non-perturbative gauge invariant definition of the Debye screening mass m_D in the effective field theory approach to finite T QCD, we use 3d lattice simulations to determine the leading O(g^2) and to estimate the next-to-leading O(g^3) corrections to m_D in the high temperature region. The O(g^2) correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD.

  2. Non-Gaussianity from isocurvature perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu; Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan); Takahashi, Fuminobu, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: nakayama@icrr.u-tokyo.ac.jp, E-mail: sekiguti@icrr.u-tokyo.ac.jp, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan)

    2008-11-15

    We develop a formalism for studying non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the cosmic microwave background temperature fluctuations, which may be confirmed in future experiments, or possibly even in the currently available observational data. As an explicit example, we consider the quantum chromodynamics axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H{sub inf} = O(10{sup 9}-10{sup 11}) GeV.

  3. A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

    Energy Technology Data Exchange (ETDEWEB)

    Lindesay, James V

    2001-05-11

    We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.

  4. Generalized perturbation theory (GPT) methods. A heuristic approach

    International Nuclear Information System (INIS)

    Gandini, A.

    1987-01-01

    Wigner first proposed a perturbation theory as early as 1945 to study fundamental quantities such as the reactivity worths of different materials. The first formulation, CPT, for conventional perturbation theory is based on universal quantum mechanics concepts. Since that early conception, significant contributions have been made to CPT, in particular, Soodak, who rendered a heuristic interpretation of the adjoint function, (referred to as the GPT method for generalized perturbation theory). The author illustrates the GPT methodology in a variety of linear and nonlinear domains encountered in nuclear reactor analysis. The author begins with the familiar linear neutron field and then generalizes the methodology to other linear and nonlinear fields, using heuristic arguments. The author believes that the inherent simplicity and elegance of the heuristic derivation, although intended here for reactor physics problems might be usefully adopted in collateral fields and includes such examples

  5. Non-perturbative string theories and singular surfaces

    International Nuclear Information System (INIS)

    Bochicchio, M.

    1990-01-01

    Singular surfaces are shown to be dense in the Teichmueller space of all Riemann surfaces and in the grasmannian. This happens because a regular surface of genus h, obtained identifying 2h disks in pairs, can be approximated by a very large genus singular surface with punctures dense in the 2h disks. A scale ε is introduced and the approximate genus is defined as half the number of connected regions covered by punctures of radius ε. The non-perturbative partition function is proposed to be a scaling limit of the partition function on such infinite genus singular surfaces with a weight which is the coupling constant g raised to the approximate genus. For a gaussian model in any space-time dimension the regularized partition function on singular surfaces of infinite genus is the partition function of a two-dimensional lattice gas of charges and monopoles. It is shown that modular invariance of the partition function implies a version of the Dirac quantization condition for the values of the e/m charges. Before the scaling limit the phases of the lattice gas may be classified according to the 't Hooft criteria for the condensation of e/m operators. (orig.)

  6. Adiabaticity and gravity theory independent conservation laws for cosmological perturbations

    Science.gov (United States)

    Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao

    2016-04-01

    We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw =cs, where δPnad = δPc,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.

  7. On the acceleration of convergence of many-body perturbation theory. Pt. 2

    International Nuclear Information System (INIS)

    Dietz, K.; Schmidt, C.; Warken, M.; Hess, B.A.

    1992-07-01

    We employ the method developed in a previous paper to small systems-Be, LiH, H 2 -where full CI-calculations are available for monitoring convergence of many-body perturbation theory. It is shown that divergent series, in particular for excited states, can be transformed into fast converging ones. In essence our method consists in performing infinite subsummations of perturbation series in order to improve convergence: coupling constants are redefined such that singularities are incorporated in a non-perturbative manner and remaining correlations can be expanded in a larger domain of the complex coupling constant plane. It is in this way that the notion of 'improved convergence' has a well defined meaning. (orig.)

  8. de Sitter limit of inflation and nonlinear perturbation theory

    DEFF Research Database (Denmark)

    R. Jarnhus, Philip; Sloth, Martin Snoager

    2007-01-01

    We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug...

  9. Axiomatic Quantum Field Theory in Terms of Operator Product Expansions: General Framework, and Perturbation Theory via Hochschild Cohomology

    Directory of Open Access Journals (Sweden)

    Stefan Hollands

    2009-09-01

    Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.

  10. Quantum Field Theory at non zero temperature

    International Nuclear Information System (INIS)

    Alvarez-Estrada, R.

    1989-01-01

    The formulations of the Φ 4 Quantum Field Theory and of Quantum Electrodynamics in I+d dimensions (d spatial dimensions) at non-zero temperature are reviewed. The behaviours of all those theories in the regime of large distances and high temperatures are surveyed. Only results are reported, all technicalities being omitted. The leading high-temperature contributions to correlation functions, to all perturbative orders, in those theories turn out to be also given by simpler theories, having much milder (superrenormalizable) ultraviolet behaviour and special mass renormalizations. In particular, the triviality/non-triviality issue for the Φ 4 theory in 1+3 dimensions is discussed briefly. (Author)

  11. High-energy behavior of non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Nieh, H.T.; Yao, Y.

    1976-01-01

    This paper is a detailed account of a study in perturbation theory of the high-energy behavior of non-Abelian gauge theories. The fermion-fermion scattering amplitude is calculated up to sixth order in the coupling constant in the high-energy limit s → infinity with fixed t, in the approximation of keeping only the leading logarithmic terms. Results indicate that the high-energy behavior of non-Abelian gauge theories are complicated, and quite different from the known behaviors of other field theories studied so far

  12. Problems of an external field in non-Abelian gauge theory

    International Nuclear Information System (INIS)

    Gavrilov, S.P.; Gitman, D.M.

    1992-01-01

    In the Abelian gauge field theory QED the principal problems connected with an external field are the problems of exact keeping of an external field in a perturbation theory and appearing in this case the peculiarities of the theory such as the instability of the vacuum and so on. There is the problem of an external field introduction or its interpretation side by side with this problem in Non-Abelian gauge theory. The solution of both these problems in Non-Abelian theory can be considered by analogy with QED. In the present paper, the authors discuss on the example of the spontaneously broken SU(2) x U(1) electroweak theory both the problems of an external field introduction and the problem of exact keeping of this field in the perturbation theory. The Langrangian of this theory in covariant gauge is chosen in the BRST invariant form. In spite of concrete character of the theory studied, the method can be extended to any gauge theory

  13. $N=2^∗$ (non-)Abelian theory in the $\\Omega$ background from string theory

    CERN Document Server

    Samsonyan, Marine; Antoniadis, Ignatios

    2018-01-01

    We present a D-brane realisation of the Abelian and non-Abelian N = 2 ∗ theory both in five and four dimensions. We compute topological amplitudes in string theory for Ω deformed spacetime first with one and then with two parameters. In the field theory limit we recover the perturbative partition function of the deformed N = 2 ∗ theory in agreement with the existing literature.

  14. Non-Gaussian statistics, classical field theory, and realizable Langevin models

    International Nuclear Information System (INIS)

    Krommes, J.A.

    1995-11-01

    The direct-interaction approximation (DIA) to the fourth-order statistic Z ∼ left-angle λψ 2 ) 2 right-angle, where λ is a specified operator and ψ is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z DIA already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (''spurious vertices'') is described. It is shown how to derive an improved representation, that realizes cumulants through O(ψ 4 ), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z DIA M to Z DIA is derived. Both Z DIA and Z DIA M incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example

  15. Perturbation theory instead of large scale shell model calculations

    International Nuclear Information System (INIS)

    Feldmeier, H.; Mankos, P.

    1977-01-01

    Results of large scale shell model calculations for (sd)-shell nuclei are compared with a perturbation theory provides an excellent approximation when the SU(3)-basis is used as a starting point. The results indicate that perturbation theory treatment in an SU(3)-basis including 2hω excitations should be preferable to a full diagonalization within the (sd)-shell. (orig.) [de

  16. Systematic Analysis of the Non-Extensive Statistical Approach in High Energy Particle Collisions—Experiment vs. Theory

    Directory of Open Access Journals (Sweden)

    Gábor Bíró

    2017-02-01

    Full Text Available The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or nuclear collisions, the number of particles is several orders of magnitude smaller than the Avogadro number; therefore, finite-size and fluctuation effects strongly influence the final-state one-particle energy distributions. Due to the simple characterization, the description of the identified hadron spectra with the Boltzmann–Gibbs thermodynamical approach is insufficient. These spectra can be described very well with Tsallis–Pareto distributions instead, derived from non-extensive thermodynamics. Using the q-entropy formula, we interpret the microscopic physics in terms of the Tsallis q and T parameters. In this paper we give a view on these parameters, analyzing identified hadron spectra from recent years in a wide center-of-mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on the center-of-mass energy and particle species (mass. Our findings are described well by a QCD (Quantum Chromodynamics inspired parton evolution ansatz. Based on this comprehensive study, apart from the evolution, both mesonic and baryonic components found to be non-extensive ( q > 1 , besides the mass ordered hierarchy observed in the parameter T. We also study and compare in details the theory-obtained parameters for the case of PYTHIA8 Monte Carlo Generator, perturbative QCD and quark coalescence models.

  17. Technical fine-tuning problem in renormalized perturbation theory

    International Nuclear Information System (INIS)

    Foda, O.E.

    1983-01-01

    The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes

  18. Technical fine-tuning problem in renormalized perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E.

    1983-01-01

    The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

  19. Non-standard perturbative methods for the effective potential in λφ4 QFT

    International Nuclear Information System (INIS)

    Okopinska, A.

    1986-07-01

    The effective potential in scalar QFT is calculated in the non-standard perturbative methods and compared with the conventional loop expansion. In the space time dimensions 0 and 1 the results are compared with the ''exact'' effective potential obtained numerically. In 4 dimensions we show that λφ 4 theory is non-interacting. (author)

  20. Non-linear perturbations of a spherically collapsing star

    International Nuclear Information System (INIS)

    Brizuela, David

    2009-01-01

    Linear perturbation theory has been a successful tool in General Relativity, and can be considered as complementary to full nonlinear simulations. Going to second and higher perturbative orders improves the approximation and offers a controlled way to analyze the nonlinearities of the theory, though the problem becomes much harder computationally. We present a systematic approach to the treatment of high order metric perturbations, focusing on the scenario of nonspherical perturbations of a dynamical spherical background. It is based on the combination of adapted geometrical variables and the use of efficient computer algebra techniques. After dealing with a number of theoretical issues, like the construction of gauge invariants, we apply the formalism to the particular case of a perfect fluid star surrounded by a vacuum exterior. We describe the regularization of the divergences of the perturbations at null infinity and the matching conditions through the surface of the star.

  1. Non-Gaussian path integration in self-interacting scalar field theories

    International Nuclear Information System (INIS)

    Kaya, Ali

    2004-01-01

    In self-interacting scalar field theories kinetic expansion is an alternative way of calculating the generating functional for Green's functions where the zeroth order non-Gaussian path integral becomes diagonal in x-space and reduces to the product of an ordinary integral at each point which can be evaluated exactly. We discuss how to deal with such functional integrals and propose a new perturbative expansion scheme which combines the elements of the kinetic expansion with the usual perturbation theory techniques. It is then shown that, when the cutoff dependences of the bare parameters in the potential are chosen to have a well defined non-Gaussian path integral without the kinetic term, the theory becomes trivial in the continuum limit

  2. Twisted boundary conditions: a non-perturbative probe for pure non-abelian gauge theories

    International Nuclear Information System (INIS)

    Baal, P. van.

    1984-01-01

    In this thesis the author describes a pure non-abelian gauge theory on the hypertorus with gauge group SU(N). To test the flux tube picture he has studied the large distance limit of this theory, leading to a large coupling constant. To tackle this problem, he describes two approaches, in both of which twisted boundary conditions play an important role. (Auth.)

  3. Bjorken-Johnson-Low technique and perturbation study on chiral anomaly in abelian coset pure gauge field theory

    International Nuclear Information System (INIS)

    Jing Sicong; Ruan Jie; AH. Dept. of Modern Physics)

    1990-01-01

    The perturbation theory in coset pure gauge field theory is studied for the first time. By using the Bjorken-johnson-Low technique and calculating the Schwinger term in related commutators, the anomalous Ward identity in Abelian coset pure gauge field theory is derived, which is consistent with the non-perutrbative calculation

  4. PWR in-core nuclear fuel management optimization utilizing nodal (non-linear NEM) generalized perturbation theory

    International Nuclear Information System (INIS)

    Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.

    1993-01-01

    The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)

  5. Fedosov quantization and perturbative quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Collini, Giovanni

    2016-12-12

    Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold (''phase space''). His algorithm gives a non-commutative, but associative, product (a so-called ''star-product'') between smooth phase space functions parameterized by Planck's constant ℎ, which is treated as a deformation parameter. In the limit as ℎ goes to zero, the star product commutator goes to ℎ times the Poisson bracket, so in this sense his method provides a quantization of the algebra of classical observables. In this work, a generalization of Fedosov's method is developed which applies to the infinite-dimensional symplectic ''manifolds'' that occur in Lagrangian field theories. We show that the procedure remains mathematically well-defined, and we explain the relationship of the method to more standard perturbative quantization schemes in quantum field theory.

  6. On the meaning of perturbation expansions in quantum field theory

    International Nuclear Information System (INIS)

    Burdik, C.; Chyla, J.

    1987-01-01

    We reformulate perturbation expansions in renormalized quantum field theories in a way that allows straightforward handling of situations when in the conventional approach (i.e. in fixed renormalization scheme) these expansions are divergent. In our approach the results of perturbation calculations of physical quantities appear in the form of (under certain circumstances) convergent expansions in powers of a free parameter χ, characterising the procedure involved. This inherent ambiguity of perturbative calculations is conjectures to be an expression of the underlaying ambiguity in the separation of the full theory into its perturbative and nonperturbative parts. The close connection of our results with the Borel summation technique is demonstrated and their relation to conventional perturbation expansions in fixed renormalization scheme is clarified

  7. Perturbation Theory of Massive Yang-Mills Fields

    Science.gov (United States)

    Veltman, M.

    1968-08-01

    Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.

  8. Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

    International Nuclear Information System (INIS)

    Hesse, Dirk

    2012-01-01

    The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

  9. Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

    Energy Technology Data Exchange (ETDEWEB)

    Hesse, Dirk

    2012-07-13

    The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

  10. Domain walls and perturbation theory in high-temperature gauge theory: SU(2) in 2+1 dimensions

    International Nuclear Information System (INIS)

    Korthals Altes, C.; Michels, A.; Teper, M.; Stephanov, M.

    1997-01-01

    We study the detailed properties of Z 2 domain walls in the deconfined high-temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both by computer simulations of the lattice theory and by one-loop perturbative calculations. The latter are carried out both in the continuum and on the lattice. We find that leading order perturbation theory reproduces the detailed properties of these domain walls remarkably accurately even at temperatures where the effective dimensionless expansion parameter g 2 /T is close to unity. The quantities studied include the surface tension, the action density profiles, roughening, and the electric screening mass. It is only for the last quantity that we find an exception to the precocious success of perturbation theory. All this shows that, despite the presence of infrared divergences at higher orders, high-T perturbation theory can be an accurate calculational tool. copyright 1997 The American Physical Society

  11. A non-perturbative approach to the Coleman-Weinberg mechanism in massless scalar QED

    International Nuclear Information System (INIS)

    Malbouisson, A.P.C.; Nogueira, F.S.; Svaiter, N.F.

    1995-08-01

    We rederived non-perturbatively the Coleman-Weinberg expression for the effective potential for massless scalar QED. Our result is not restricted to small values of the coupling constants. This shows that the Coleman-Weinberg result can be established beyond the range of perturbation theory. Also, we derive it in a manifestly renormalization group invariant way. It is shown that with the derivation given no Landau ghost singularity arises. The finite temperature case is discussed. (author). 13 refs

  12. Perturbative Gravity and Gauge Theory Relations: A Review

    Directory of Open Access Journals (Sweden)

    Thomas Søndergaard

    2012-01-01

    Full Text Available This paper is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular, the field theory part is based on some very recent developments.

  13. Application of the perturbation theory for sensitivity calculations in thermalhydraulics reactor calculations

    International Nuclear Information System (INIS)

    Andrade Lima, F.R. de

    1986-01-01

    The sensitivity of non linear responses associated with physical quantities governed by non linear differential systems can be studied using perturbation theory. The equivalence and formal differences between the differential and GPT formalisms are shown and both are used for sensitivity calculations of transient problems in a typical PWR coolant channel. The results obtained are encouraging with respect to the potential of the method for thermalhydraulics calculations normally performed for reactor design and safety analysis. (Author) [pt

  14. Perturbing the ground ring of 2D string theory

    CERN Document Server

    Barbón, José L F

    1992-01-01

    We use free field techniques in D=2 string theory to calculate the perturbation of the special state algebras when the cosmologi- cal constant is turned on. In particular, we find that the "ground cone" preserved by the ring structure is promoted to a three dimen- sional hyperboloid as conjectured by Witten. On the other hand, the perturbed (1,1) a three dimensional hyperboloid as conjectured by Witten. On the other hand, the perturbed (1,1) current algebra of moduli deformations is computed completely, and no simple geometrical inter- pretation is found. We also quote some facts concerning the Liouville/matrix model dictio- nary in this class of theories.

  15. Acoustic anisotropic wavefields through perturbation theory

    KAUST Repository

    Alkhalifah, Tariq Ali

    2013-01-01

    these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing

  16. Principles of chiral perturbation theory

    International Nuclear Information System (INIS)

    Leutwyler, H.

    1995-01-01

    An elementary discussion of the main concepts used in chiral perturbation theory is given in textbooks and a more detailed picture of the applications may be obtained from the reviews. Concerning the foundations of the method, the literature is comparatively scarce. So, I will concentrate on the basic concepts and explain why the method works. (author)

  17. Excitation energies from Görling-Levy perturbation theory along the range-separated adiabatic connection

    Science.gov (United States)

    Rebolini, Elisa; Teale, Andrew M.; Helgaker, Trygve; Savin, Andreas; Toulouse, Julien

    2018-06-01

    A Görling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionisation energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.

  18. Horizon-preserving dualities and perturbations in non-canonical scalar field cosmologies

    International Nuclear Information System (INIS)

    Geshnizjani, Ghazal; Kinney, William H.; Dizgah, Azadeh Moradinezhad

    2012-01-01

    We generalize the cosmological duality between inflation and cyclic contraction under the interchange a↔H to the case of non-canonical scalar field theories with varying speed of sound. The single duality in the canonical case generalizes to a family of three dualities constructed to leave the cosmological acoustic horizon invariant. We find three classes of models: (I) DBI inflation, (II) the non-canonical generalization of cyclic contraction, and (III) a new cosmological solution with rapidly decreasing speed of sound and relatively slowly growing scale factor, which we dub stalled cosmology. We construct dual analogs to the inflationary slow roll approximation, and solve for the curvature perturbation in all three cases. Both cyclic contraction and stalled cosmology predict a strongly blue spectrum for the curvature perturbations inconsistent with observations

  19. Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation

    International Nuclear Information System (INIS)

    Pletzer, A.; Zakharov, L.E.

    1999-01-01

    The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory

  20. Exact Results in Non-Supersymmetric Large N Orientifold Field Theories

    CERN Document Server

    Armoni, Adi; Veneziano, Gabriele

    2003-01-01

    We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N=1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N).

  1. Energy momentum tensor in local causal perturbation theory

    International Nuclear Information System (INIS)

    Prange, D.

    2001-01-01

    We study the energy momentum tensor in the Bogolyubov-Epstein-Glaser approach to perturbation theory. It is found to be locally conserved for a class of theories containing to derivated fields in the interaction. For the massless φ 4 -theory we derive the trace anomaly of the improved tensor. (orig.)

  2. Perturbative and global anomalies in supergravity theories

    International Nuclear Information System (INIS)

    Sezgin, E.

    1986-09-01

    Perturbative and global anomalies in supergravity theories are reviewed. The existence of a matter and gauge coupled supergravity theory in six dimensions with E 6 xE 7 xU(1) symmetry and highly nontrivial anomaly cancellations is emphasised. The possible string origin of this theory is posed as an open problem, study of which may lead to discovery of new ways to construct/compactify heterotic superstrings. (author)

  3. New hybrid non-linear transformations of divergent perturbation series for quadratic Zeeman effects

    International Nuclear Information System (INIS)

    Belkic, D.

    1989-01-01

    The problem of hydrogen atoms in an external uniform magnetic field (quadratic Zeeman effect) is studied by means of perturbation theory. The power series for the ground-state energy in terms of magnetic-field strength B is divergent. Nevertheless, it is possible to induce convergence of this divergent series by applying various non-linear transformations. These transformations of originally divergent perturbation series yield new sequences, which then converge. The induced convergence is, however, quite slow. A new hybrid Shanks-Levin non-linear transform is devised here for accelerating these slowly converging series and sequences. Significant improvement in the convergence rate is obtained. Agreement with the exact results is excellent. (author)

  4. Non-adiabatic perturbations in Ricci dark energy model

    International Nuclear Information System (INIS)

    Karwan, Khamphee; Thitapura, Thiti

    2012-01-01

    We show that the non-adiabatic perturbations between Ricci dark energy and matter can grow both on superhorizon and subhorizon scales, and these non-adiabatic perturbations on subhorizon scales can lead to instability in this dark energy model. The rapidly growing non-adiabatic modes on subhorizon scales always occur when the equation of state parameter of dark energy starts to drop towards -1 near the end of matter era, except that the parameter α of Ricci dark energy equals to 1/2. In the case where α = 1/2, the rapidly growing non-adiabatic modes disappear when the perturbations in dark energy and matter are adiabatic initially. However, an adiabaticity between dark energy and matter perturbations at early time implies a non-adiabaticity between matter and radiation, this can influence the ordinary Sachs-Wolfe (OSW) effect. Since the amount of Ricci dark energy is not small during matter domination, the integrated Sachs-Wolfe (ISW) effect is greatly modified by density perturbations of dark energy, leading to a wrong shape of CMB power spectrum. The instability in Ricci dark energy is difficult to be alleviated if the effects of coupling between baryon and photon on dark energy perturbations are included

  5. Gravitational perturbation theory and synchrotron radiation

    Energy Technology Data Exchange (ETDEWEB)

    Breuer, R A [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany). Inst. fuer Astrophysik

    1975-01-01

    This article presents methods and results for a gravitational perturbation theory which treats massless fields as linearized perturbations of an arbitrary gravitational vacuum background spacetime. The formalism is outlined for perturbations of type (22) spacetimes. As an application, high-frequency radiation emitted by particles moving approximately on relativistic circular geodesic orbits is computed. More precisely, the test particle assumption is made; throughout it is therefore assumed that the reaction of the radiation on the particle motion is negligible. In particular, these orbits are studied in the gravitational field of a spherically symmetric (Schwarzschild-) black hole as well as of a rotating (Kerr-) black hole. In this model, the outgoing radiation is highly focussed and of much higher fequency than the orbital frequency, i.e. one is dealing with 'gravitational synchrotron radiation'.

  6. Gribov ambiguity, perturbation theory, and confinement

    International Nuclear Information System (INIS)

    Greensite, J.P.

    1978-01-01

    The generating functional proposed for gauge theories by Bender, Eguchi, and Pagels (BEP) is shown to be equivalent to a truncated form of the functional integral, in which only one field configuration from each gauge-equivalent Gribov set contributes to the functional integration. The standard perturbation technique provides a method of realizing this truncation condition. It is shown that any gauge-covariant quantity (such as the quark N-point functions), evaluated by perturbating around a field configuration gauge-equivalent to A = 0, is related by a gauge transformation to the same quantity evaluated perturbatively around the trivial vacuum. It follows that, contrary to the conclusion of BEP, the existence of degeneracies in the Coulomb gauge-fixing condition (the Gribov ambiguity) is not directly related to the physics of confinement

  7. Statistical Learning Theory: Models, Concepts, and Results

    OpenAIRE

    von Luxburg, Ulrike; Schoelkopf, Bernhard

    2008-01-01

    Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. This paper can serve as a starting point for people who want to get an overview on the field before diving into technical details.

  8. Some aspects of non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Tyburski, L.J.

    1976-01-01

    Two aspects of the theory of non-Abelian gauge fields are considered. In the first part, the fermion-fermion scattering amplitude is calculated for a non-Abelian gauge theory with SU(N) gauge symmetry in the limit of high energy with fixed momentum transfer through sixth order in the coupling constant. Only the leading logarithmic terms in each order of perturbation theory are kept. To avoid the infrared problem, the Higgs mechanism is invoked to give masses to the vector bosons of the theory. It is found that the scattering amplitude exponentiates to a Regge form. This result is qualitatively different from an earlier published calculation. In the second part of the thesis, we consider fermion-fermion scattering in a non-Abelian gauge theory with massless vector bosons, and demonstrate that for physically measurable cross sections the infrared divergences of the theory cancel out to lowest nontrivial order

  9. Photoionization cross sections and Auger rates calculated by many-body perturbation theory

    International Nuclear Information System (INIS)

    Kelly, H.P.

    1976-01-01

    Methods for applying the many body perturbation theory to atomic calculations are discussed with particular emphasis on calculation of photoionization cross sections and Auger rates. Topics covered include: Rayleigh--Schroedinger theory; many body perturbation theory; calculations of photoionization cross sections; and Auger rates

  10. M{sub b} and f{sub B} from non-perturbatively renormalized HQET with N{sub f} = 2 light quarks

    Energy Technology Data Exchange (ETDEWEB)

    Blossier, Benoit [CNRS et Univ. Paris-Sud XI, Orsay (France). Lab. de Physique Theorique; Bulava, John [CERN, Geneva (Switzerland). Physics Dept.; Della Morte, Michele; Hippel, Georg von [Mainz Univ. (Germany). Inst. fuer Kernphysik; Donnellan, Michael; Simma, Hubert; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). NIC; Fritzsch, Patrick [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Garron, Nicolas [Edinburgh Univ. (United Kingdom). Tait Inst.; Heitger, Jochen [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1

    2011-12-15

    We present an updated analysis of the non-perturbatively renormalized b-quark mass and B meson decay constant based on CLS lattices with two dynamical non-perturbatively improved Wilson quarks. This update incorporates additional light quark masses and lattice spacings in large physical volume to improve chiral extrapolations and to reach the continuum limit. We use Heavy Quark Effective Theory (HQET) including 1/m{sub b} terms with non-perturbative coefficients based on the matching of QCD and HQET developed by the ALPHA collaboration during the past years. (orig.)

  11. Non-perturbative heavy quark effective theory. An application to semi-leptonic B-decays

    International Nuclear Information System (INIS)

    Della Morte, Michele; Heitger, Jochen; Simma, Hubert; Sommer, Rainer; Humboldt-Universitaet, Berlin

    2015-01-01

    We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m h -corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays at the leading order in 1/m h .

  12. Inflation and the theory of cosmological perturbations

    International Nuclear Information System (INIS)

    Riotto, A.

    2003-01-01

    These lectures provide a pedagogical introduction to inflation and the theory of cosmological perturbations generated during inflation which are thought to be the origin of structure in the universe. (author)

  13. Factorization theorems in perturbative quantum field theory

    International Nuclear Information System (INIS)

    Date, G.D.

    1982-01-01

    This dissertation deals with factorization properties of Green functions and cross-sections in perturbation theory. It consists of two parts. Part I deals with the factorization theorem for the Drell-Yan cross-section. The new approach developed for this purpose is based upon a renormalization group equation with a generalized anomalous dimension. Using an alternate form of factorization for the Drell-Yan cross-section, derived in perturbation theory, a corresponding generalized anomalous dimension is defined, and explicit Feynman rules for its calculation are given. The resultant renormalization group equation is solved by a formal solution which is exhibited explicitly. Simple, explicit calculations are performed which verify Mueller's conjecture for the recovery of the usual parton model results for the Drell-Yan cross-section. The approach developed in this work offers a general framework to analyze the role played by the group factors in the cancellation of the soft divergences, and study their influence on the asymptotic behavior. Part II deals with factorization properties of the Green functions in position space. In this part, a Landau equation analysis is carried out for the singularities of the position space Green fucntions, in perturbation theory with the theta 4 interaction Lagrangian. A physical picture interpretation is given for the corresponding Landau equations. It is used to suggest a light-cone expansion. Using a power counting method, a formal derivation of the light-cone expansion for the two point function, the three point function and a product of two currents, is given without assuming a short distance expansion. Possible extensions to other theories is also considered

  14. Fractional analytic perturbation theory in Minkowski space and application to Higgs boson decay into a bb pair

    International Nuclear Information System (INIS)

    Bakulev, A. P.; Mikhailov, S. V.; Stefanis, N. G.

    2007-01-01

    We work out and discuss the Minkowski version of fractional analytic perturbation theory for QCD observables, recently developed and presented by us for the Euclidean region. The original analytic approach to QCD, initiated by Shirkovand Solovtsov, is summarized and relations to other proposals to achieve an analytic strong coupling are pointed out. The developed framework is applied to the Higgs boson decay into a bb pair, using recent results for the massless correlator of two quark scalar currents in the MS scheme.We present calculations for the decay width within the Minkowski version off ractional analytic perturbation theory including those non-power-series contributions that correspond to the O(α s 3 )-terms, also taking into account evolution effects of the running coupling and the b-quark-mass renormalization. Comparisons with previous results within standard QCD perturbation theory are performed and the differences are pointed out. The interplay between effects originating from the analyticity requirement and the analytic continuation from the spacelike to the timelike region and those due to the evolution of the heavy-quark mass is addressed, highlighting the differences from the conventional QCD perturbation theory

  15. An improved thermodynamic perturbation theory for Mercedes-Benz water.

    Science.gov (United States)

    Urbic, T; Vlachy, V; Kalyuzhnyi, Yu V; Dill, K A

    2007-11-07

    We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.

  16. Perturbation theory via Feynman diagrams in classical mechanics

    OpenAIRE

    Penco, R.; Mauro, D.

    2006-01-01

    In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.

  17. S-matrices for perturbations of certain conformal field theories

    International Nuclear Information System (INIS)

    Freund, P.G.O.; Klassen, T.R.; Melzer, E.; Chicago Univ., IL

    1989-01-01

    We present a family of factorizable S-matrix theories in 1+1 dimensions with an arbitrary number N of particles of distinct masses, and find the conservation laws of these theories. An analysis of the conservation laws of the family of nonunitary CFTs with central charge c=c 2,2N+3 =-2N(6N+5)/(2N+3) perturbed by the φ (1,3) operator, leads us to conjecture the identification of these perturbed CFTs with the S-matrix theories we found. The case N=1 was treated by Cardy and Mussardo. We also present the S-matrix of an E 7 -related unitary model. (orig.)

  18. Perturbation theories for the dipolar fluids

    International Nuclear Information System (INIS)

    Lee, L.L.; Chung, T.H.

    1983-01-01

    We derive here four different perturbation equations for the calculation of the angular pair correlation functions of dipolar fluids; namely, the first order y-expansion, the modified Percus--Yevik (MPY) expansion, the modified hypernetted chain (MHNC) expansion, and the modified linearized hypernetted chain (MLHNC) equation. Both the method of the functional expansion and the method of the cluster integrals are utilized. Comparison with other perturbation theories (e.g., the Melnyk--Smith equation) is made. While none of the theories is exact, as shown by the cluster diagrams, the MLHNC and the MHNC contain more diagrams than, say, the MPY and y-expansion. The y-expansion equation can be improved by including the correction terms to the Kirkwood superposition approximation for the triplet correlation function. For example, the inclusion of the correction term rho∫d4h(14)h(24)h(34) in a formula given by Henderson, is shown to improve substantially the y-expansion equation. We examine the performance of two of the theories: the y-expansion and the MLHNC equation for a Stockmayer (dipolar) fluid with a reduced dipole moment μ/sup asterisk2/ [ = μ 2 /(epsilonsigma 3 )] = 1.0. Comparison with Monte Carlo simulation results of Adams et al. and with other theories (e.g., the QHNC equation) shows that our results are reasonable. Further improvements of the equations are also pointed out

  19. Non-commutative field theory with twistor-like coordinates

    International Nuclear Information System (INIS)

    Taylor, Tomasz R.

    2007-01-01

    We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual twistors, quantum theory of fields described by non-holomorphic functions of twistor variables becomes manifestly non-commutative, with Lorentz symmetry broken by a time-like vector. We discuss the free field propagation and its impact on the short- and long-distance behavior of physical amplitudes in perturbation theory. In the ultraviolet limit, quantum field theories in twistor space are generically less divergent than their commutative counterparts. Furthermore, there is no infrared-ultraviolet mixing problem

  20. 1/N perturbation theory and quantum conservation laws for supersymmetrical chiral field. 2

    International Nuclear Information System (INIS)

    Aref'eva, I.Ya.; Krivoshchekov, V.K.; Medvedev, P.B.; Gosudarstvennyj Komitet Standartov Soveta Ministrov SSSR, Moscow; Gosudarstvennyj Komitet po Ispol'zovaniyu Atomnoj Ehnergii SSSR, Moscow. Inst. Teoreticheskoj i Ehksperimental'noj Fiziki)

    1980-01-01

    The renormalizability of the supersymmetric chiral model (supersymmetric nonlinear σ-model) is proved in the framework of the 1/N perturbation theory expansion proposed in the previous paper. The renormalizability proof is essentially based on the quantum supersymmetric chirality condition. The supersymmetric formulation of equations of motion is given. The first non-trivial quantum conservation laws are derived

  1. Fundamental parameters of QCD from non-perturbative methods for two and four flavors

    International Nuclear Information System (INIS)

    Marinkovic, Marina

    2013-01-01

    The non-perturbative formulation of Quantumchromodynamics (QCD) on a four dimensional space-time Euclidean lattice together with the finite size techniques enable us to perform the renormalization of the QCD parameters non-perturbatively. In order to obtain precise predictions from lattice QCD, one needs to include the dynamical fermions into lattice QCD simulations. We consider QCD with two and four mass degenerate flavors of O(a) improved Wilson quarks. In this thesis, we improve the existing determinations of the fundamental parameters of two and four flavor QCD. In four flavor theory, we compute the precise value of the Λ parameter in the units of the scale L max defined in the hadronic regime. We also give the precise determination of the Schroedinger functional running coupling in four flavour theory and compare it to the perturbative results. The Monte Carlo simulations of lattice QCD within the Schroedinger Functional framework were performed with a platform independent program package Schroedinger Funktional Mass Preconditioned Hybrid Monte Carlo (SF-MP-HMC), developed as a part of this project. Finally, we compute the strange quark mass and the Λ parameter in two flavour theory, performing a well-controlled continuum limit and chiral extrapolation. To achieve this, we developed a universal program package for simulating two flavours of Wilson fermions, Mass Preconditioned Hybrid Monte Carlo (MP-HMC), which we used to run large scale simulations on small lattice spacings and on pion masses close to the physical value.

  2. Lie transforms and their use in Hamiltonian perturbation theory

    International Nuclear Information System (INIS)

    Cary, J.R.

    1978-06-01

    A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here

  3. Screening of Coulomb interaction and many-body perturbation theory in atoms

    International Nuclear Information System (INIS)

    Dzyuba, V.A.; Flambaum, V.V.; Sil'vestrov, P.G.; Sushkov, O.P.

    1988-01-01

    Taking into account the electron Coulomb interaction screening considerably improves the convergence of perturbation theory in residual interaction. The developed technique allows to take into account screening diagrams in all orders of perturbation theory. Calculation of the correlation corrections to the thallium energy levels is carried out as an example

  4. Linear and non-linear amplification of high-mode perturbations at the ablation front in HiPER targets

    Energy Technology Data Exchange (ETDEWEB)

    Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)

    2011-01-15

    The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.

  5. A new perturbative approximation applied to supersymmetric quantum field theory

    International Nuclear Information System (INIS)

    Bender, C.M.; Milton, K.A.; Pinsky, S.S.; Simmons, L.M. Jr.; Los Alamos National Lab.

    1988-01-01

    We show that a recently proposed graphical perturbative calculational scheme in quantum field theory is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not known of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

  6. Implementation of static generalized perturbation theory for LWR design applications

    International Nuclear Information System (INIS)

    Byron, R.F.; White, J.R.

    1987-01-01

    A generalized perturbation theory (GPT) formulation is developed for application to light water reactor (LWR) design. The extensions made to standard generalized perturbation theory are the treatment of thermal-hydraulic and fission product poisoning feedbacks, and criticality reset. This formulation has been implemented into a standard LWR design code. The method is verified by comparing direct calculations with GPT calculations. Data are presented showing that feedback effects need to be considered when using GPT for LWR problems. Some specific potential applications of this theory to the field of LWR design are discussed

  7. Perturbative algebraic quantum field theory an introduction for mathematicians

    CERN Document Server

    Rejzner, Kasia

    2016-01-01

    Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are th...

  8. Exploring perturbative conformal field theory in Mellin space

    Energy Technology Data Exchange (ETDEWEB)

    Nizami, Amin A. [International Centre for Theoretical Sciences, TIFR,Hesaraghatta, Hubli, Bengaluru-560089 (India); Rudra, Arnab [Center for Quantum Mathematics and Physics (QMAP), Department of Physics,University of California, Davis, 1 Shields Ave, Davis, CA 95616 (United States); Sarkar, Sourav [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, IRIS-Adlershof,Zum Großen Windkanal 6, 12489 Berlin (Germany); Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, 14476 Potsdam (Germany); Verma, Mritunjay [International Centre for Theoretical Sciences, TIFR,Hesaraghatta, Hubli, Bengaluru-560089 (India); Harish-Chandra Research Institute,Chhatnag Road, Jhunsi, Allahabad-211019 (India)

    2017-01-24

    We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.

  9. Non-perturbative QCD and hadron physics

    International Nuclear Information System (INIS)

    Cobos-Martínez, J J

    2016-01-01

    A brief exposition of contemporary non-perturbative methods based on the Schwinger-Dyson (SDE) and Bethe-Salpeter equations (BSE) of Quantum Chromodynamics (QCD) and their application to hadron physics is given. These equations provide a non-perturbative continuum formulation of QCD and are a powerful and promising tool for the study of hadron physics. Results on some properties of hadrons based on this approach, with particular attention to the pion distribution amplitude, elastic, and transition electromagnetic form factors, and their comparison to experimental data are presented. (paper)

  10. Non-perturbative QCD correlation functions

    Energy Technology Data Exchange (ETDEWEB)

    Cyrol, Anton Konrad

    2017-11-27

    Functional methods provide access to the non-perturbative regime of quantum chromo- dynamics. Hence, they allow investigating confinement and chiral symmetry breaking. In this dissertation, correlation functions of Yang-Mills theory and unquenched two-flavor QCD are computed from the functional renormalization group. Employing a self-consistent vertex expansion of the effective action, Yang-Mills correlation functions are obtained in four as well as in three spacetime dimensions. To this end, confinement and Slavnov-Taylor identities are discussed. Our numerical results show very good agreement with corresponding lattice results. Next, unquenched two-flavor QCD is considered where it is shown that the unquenched two-flavor gluon propagator is insensitive to the pion mass. Furthermore, the necessity for consistent truncations is emphasized. Finally, correlation functions of finite-temperature Yang-Mills theory are computed in a truncation that includes the splitting of the gluon field into directions that are transverse and longitudinal to the heat bath. In particular, it includes the splitting of the three- and four-gluon vertices. The obtained gluon propagator allows to extract a Debye screening mass that coincides with the hard thermal loop screening mass at high temperatures, but is meaningful also at temperatures below the phase transition temperature.

  11. Perturbation theory with instantons

    International Nuclear Information System (INIS)

    Carruthers, P.; Pinsky, S.S.; Zachariasen, F.

    1977-05-01

    ''Perturbation theory'' rules are developed for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the ''dilute gas'' approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form (μ 2 /q 2 )/sup -8π 2 b/ where b is the coefficient in the expansion of the β function: β = bg 3 +...

  12. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces

    International Nuclear Information System (INIS)

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-01-01

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of “statistical associating fluid theory” that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH 2 and CH 3 and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ∼2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ∼1% from simulation data while the theory reproduces

  13. Acoustic anisotropic wavefields through perturbation theory

    KAUST Repository

    Alkhalifah, Tariq Ali

    2013-09-01

    Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.

  14. Regular perturbation theory for two-electron atoms

    International Nuclear Information System (INIS)

    Feranchuk, I.D.; Triguk, V.V.

    2011-01-01

    Regular perturbation theory (RPT) for the ground and excited states of two-electron atoms or ions is developed. It is shown for the first time that summation of the matrix elements from the electron-electron interaction operator over all intermediate states can be calculated in a closed form by means of the two-particle Coulomb Green's function constructed in the Letter. It is shown that the second order approximation of RPT includes the main part of the correlation energy both for the ground and excited states. This approach can be also useful for description of two-electron atoms in external fields. -- Highlights: → We develop regular perturbation theory for the two-electron atoms or ions. → We calculate the sum of the matrix elements over all intermediate states. → We construct the two-particle Coulomb Green's function.

  15. Limiting processes in non-equilibrium classical statistical mechanics

    International Nuclear Information System (INIS)

    Jancel, R.

    1983-01-01

    After a recall of the basic principles of the statistical mechanics, the results of ergodic theory, the transient at the thermodynamic limit and his link with the transport theory near the equilibrium are analyzed. The fundamental problems put by the description of non-equilibrium macroscopic systems are investigated and the kinetic methods are stated. The problems of the non-equilibrium statistical mechanics are analyzed: irreversibility and coarse-graining, macroscopic variables and kinetic description, autonomous reduced descriptions, limit processes, BBGKY hierarchy, limit theorems [fr

  16. Non-linearity consideration when analyzing reactor noise statistical characteristics. [BWR

    Energy Technology Data Exchange (ETDEWEB)

    Kebadze, B V; Adamovski, L A

    1975-06-01

    Statistical characteristics of boiling water reactor noise in the vicinity of stability threshold are studied. The reactor is considered as a non-linear system affected by random perturbations. To solve a non-linear problem the principle of statistical linearization is used. It is shown that the halfwidth of resonance peak in neutron power noise spectrum density as well as the reciprocal of noise dispersion, which are used in predicting a stable operation theshold, are different from zero both within and beyond the stability boundary the determination of which was based on linear criteria.

  17. Chiral perturbation theory for lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Baer, Oliver

    2010-07-21

    The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)

  18. Chiral perturbation theory for lattice QCD

    International Nuclear Information System (INIS)

    Baer, Oliver

    2010-01-01

    The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)

  19. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces

    Science.gov (United States)

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-07-01

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of "statistical associating fluid theory" that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH2 and CH3 and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ˜2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ˜1% from simulation data while the theory reproduces the excess

  20. Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field

    International Nuclear Information System (INIS)

    Zhao-Long, Liu; Hai-Yun, Hu; Tian-You, Fan; Xiu-San, Xing

    2010-01-01

    This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of micro-crack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field. (cross-disciplinary physics and related areas of science and technology)

  1. Perturbing the ground ring of 2D string theory

    International Nuclear Information System (INIS)

    Barbon, J.L.F.

    1992-01-01

    In this paper, the authors use free field techniques in D = 2 string theory t calculate the perturbation of the special state algebras when the cosmological constant is turned on. In particular, the authors find that the 'ground cone' preserved by the ring structure is promoted to a three-dimensional hyperboloid as conjectured by Witten. On the other hand, the perturbed (1,1) current algebra of moduli deformations is computed completely, and no simple geometrical interpretation is found. The authors also quote some facts concerning the Liouville matrix a model dictionary in this class of theories

  2. Modified potentials in many-body perturbation theory

    International Nuclear Information System (INIS)

    Silver, D.M.; Bartlett, R.J.

    1976-01-01

    Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-V/sup N/ potential

  3. Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

    Science.gov (United States)

    Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

    2015-10-02

    The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

  4. Braking due to non-resonant magnetic perturbations and comparison with neoclassical toroidal viscosity torque in EXTRAP T2R

    Science.gov (United States)

    Frassinetti, L.; Sun, Y.; Fridström, R.; Menmuir, S.; Olofsson, K. E. J.; Brunsell, P. R.; Khan, M. W. M.; Liang, Y.; Drake, J. R.

    2015-09-01

    The non-resonant magnetic perturbation (MP) braking is studied in the EXTRAP T2R reversed-field pinch (RFP) and the experimental braking torque is compared with the torque expected by the neoclassical toroidal viscosity (NTV) theory. The EXTRAP T2R active coils can apply magnetic perturbations with a single harmonic, either resonant or non-resonant. The non-resonant MP produces velocity braking with an experimental torque that affects a large part of the core region. The experimental torque is clearly related to the plasma displacement, consistent with a quadratic dependence as expected by the NTV theory. The work show a good qualitative agreement between the experimental torque in a RFP machine and NTV torque concerning both the torque density radial profile and the dependence on the non-resonant MP harmonic.

  5. Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

    International Nuclear Information System (INIS)

    Zavaljevski, N.

    1985-01-01

    Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

  6. Non-perturbative approach to 2D-supergravity and super-Virasoro constraints

    CERN Document Server

    Becker, M

    1994-01-01

    The coupling of N=1 SCFT of type (4m,2) to two-dimensional supergravity can be formulated non-perturbatively in terms of a discrete super-eigenvalue model proposed by Alvarez-Gaum\\'e, et al. We derive the superloop equations that describe, in the double scaling limit, the non-perturbative solution of this model. These equations are equivalent to the double scaled super-Virasoro constraints satisfied by the partition function. They are formulated in terms of a \\widehat c=1 theory, with a \\IZ_2-twisted scalar field and a Weyl-Majorana fermion in the Ramond sector. We have solved the superloop equations to all orders in the genus expansion and obtained the explicit expressions for the correlation functions of gravitationally dressed scaling operators in the NS- and R-sector. In the double scaling limit, we obtain a formulation of the model in terms of a new supersymmetric extension of the KdV hierarchy.

  7. Perturbation theory and nonperturbative effects: a happy marriage?

    International Nuclear Information System (INIS)

    Chyla, J.

    1992-01-01

    Perturbation expansions in renormalized quantum theories are reformulated in a way that permits a straightforward handling of situations when in the conventional approach, i.e. in fixed renormalization scheme, these expansions are factorially divergent and even of asymptotically constant sign. The result takes the form of convergent (under certain circumstances) expansions in a set of functions Z k (a,χ) of the couplant and the free parameter χ specifies the procedure involved. The value of χ is shown to be correlated to the basic properties of nonperturbative effects as embodied in power corrections. A close connection of this procedure to the Borel summation technique is demonstrated and its relation to conventional perturbation theory in fixed renormalization schemes elucidated. (author) 3 figs., 17 refs

  8. Algebraic quantum field theory, perturbation theory, and the loop expansion

    International Nuclear Information System (INIS)

    Duetsch, M.; Fredenhagen, K.

    2001-01-01

    The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A (n) of observables ''up to n loops'', where A (0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. (orig.)

  9. Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes

    International Nuclear Information System (INIS)

    Nagar, Alessandro; Rezzolla, Luciano

    2005-01-01

    The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this review is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of a Schwarzschild black-hole spacetime driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes. (topical review)

  10. The Rise and Fall of the Cosmic String Theory for Cosmological Perturbations

    International Nuclear Information System (INIS)

    Perivolaropoulos, L.

    2005-01-01

    The cosmic string theory for cosmological fluctuations is a good example of healthy scientific progress in cosmology. It is a well defined physically motivated model that has been tested by cosmological observations and has been ruled out as a primary source of primordial fluctuations. Until about fifteen years ago, the cosmic string theory of cosmological perturbations provided one of the two physically motivated candidate theories for the generation of primordial perturbations. The cosmological data that appeared during the last decade have been compared with the well defined predictions of the theory and have ruled out cosmic strings as a primary source of primordial cosmological perturbations. Since cosmic strings are predicted to form after inflation in a wide range of microphysical theories (including supersymmetric and fundamental string theories) their observational bounds may serve a source of serious constraints for these theories. This is a pedagogical review of the historical development, the main predictions of the cosmic string theory and the constraints that have been imposed on it by cosmological observations. Recent lensing events that could be attributed to lighter cosmic strings are also discussed

  11. Perturbation theory of intermolecular interactions: What is the problem, are there solutions?

    International Nuclear Information System (INIS)

    Adams, W.H.

    1990-01-01

    We review the nature of the problem in the framework of Rayleigh-Schroedinger perturbation theory (the polarization approximation) considering explicitly two examples: the interaction of two hydrogen atoms and the interaction of Li with H. We show, in agreement with the work of Claverie and of Morgan and Simon, that the LiH problem is dramatically different from the H 2 problem. In particular, the physical states of LiH are higher in energy than an infinite number of discrete, unphysical states and they are buried in a continuum of unbound, unphysical states, which starts well below the lowest physical state. Clavrie has shown that the perturbation expansion, under these circumstances, is likely to converge to an unphysical state of lower energy than the physical ground state, if it converges at all. We review, also, the application of two classes of exchange perturbation theory to LiH and larger systems. We show that the spectra of three Eisenschitz-London (EL) class, exchange perturbation theories have no continuum of unphysical states overlaying the physical states and no discrete, unphysical states below the lowest physical state. In contrast, the spectra of two Hirschfelder-Silbey class theories differ hardly at all from that found with the polarization approximation. Not one of the EL class of perturbation theories, however, eliminates all of the discrete unphysical states

  12. New perturbative approach to renormalizable field theories

    International Nuclear Information System (INIS)

    Dhar, A.; Gupta, V.

    1984-01-01

    A new method for obtaining perturbative predictions in quantum field theory is developed. Our method gives finite predictions, which are free from scheme ambiguities, for any quantity of interest (like a cross section or a Green's function) starting directly from the bare regularized Lagrangian. The central idea in our approach is to incorporate directly the consequences of dimensional transmutation for the predictions of the theory. We thus completely bypass the conventional renormalization procedure and the ambiguities associated with it. The case of massless theories with a single dimensionless coupling constant is treated in detail to illustrate our approach

  13. A non-perturbative approach to strings

    International Nuclear Information System (INIS)

    Orland, P.

    1986-03-01

    After briefly reviewing the theory of strings in the light-cone gauge, a lattice regularized path integral for the amplitudes is discussed. The emphasis is put on a toy string model; the U(N) Veneziano model in the limit as N->infinite with g 0 2 N fixed. The lattice methods of Giles and Thorn are used extensively, but are found to require modification beyond perturbation theory. The twenty-six-dimensional toy string model is recast as a two-dimensional spin system. (orig.)

  14. Algebraic perturbation theory for dense liquids with discrete potentials

    Science.gov (United States)

    Adib, Artur B.

    2007-06-01

    A simple theory for the leading-order correction g1(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g1(r) . The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.

  15. The calculation of isotopic partition function ratios by a perturbation theory technique

    International Nuclear Information System (INIS)

    Singh, G.; Wolfsberg, M.

    1975-01-01

    The vibrational Hamiltonian of a molecule in the harmonic approximation, H = (1/2) Σ (g/subi/jp/subi/p/subj/ + f/subi/jq/subi/q/subj/), has been divided into a diagonal part (terms with i=j) and an off-diagonal part (inot-equalj), which is regarded as the perturbation. The vibrational partition function of the molecule is then calculated by Schwinger perturbation theory as the partition function of the unperturbed problem, corresponding to a collection of oscillators with frequencies 2πν/subi/' = (f/subi/ig/subi/i)/sup 1 / 2 /, plus perturbation correction terms which are calculated to second order. With the usual assumptions of isotope effect calculations that the molecular translations and rotations are classical and separable from the vibrations, the perturbation formulation of the vibrational partition function is easily transformed into a perturbation theory formulation of (reduced) isotopic partition function ratios. If, for example, the molecular potential function is expressed in terms of the displacements of bond stretches and bond angle bends from their respective equilibrium values, the unperturbed partition function ratio corresponds to the isotope effect expected for noninteracting bond-stretch and bond-angle-bend oscillators. Detailed comparison is made for a number of molecular systems of perturbation theory calculations of partition functions and isotopic partition function ratios with exact calculations carried out by actually obtaining the normal mode vibrational frequencies of the vibrational Hamiltonian. Good agreement is found. The utility of the perturbation theory formulation resides in the fact that it permits one to look at isotope effects in a very simple manner; some demonstrations are given

  16. On the predictivity of the non-renormalizable quantum field theories

    Energy Technology Data Exchange (ETDEWEB)

    Pittau, Roberto [CERN, PH-TH, Geneva (Switzerland)

    2015-02-01

    Following a Four Dimensional Renormalization approach to ultraviolet divergences (FDR), we extend the concept of predictivity to non-renormalizable quantum field theories at arbitrarily large perturbative orders. The idea of topological renormalization is introduced, which keeps a finite value for the parameters of the theory by trading the usual order-by-order renormalization procedure for an order-by-order redefinition of the perturbative vacuum. One additional measurement is then sufficient to systematically compute quantum corrections at any loop order, with no need of absorbing ultraviolet infinities in the Lagrangian. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  17. Application of perturbation theory to the non-linear vibration analysis of a string including the bending moment effects

    International Nuclear Information System (INIS)

    Esmaeilzadeh Khadem, S.; Rezaee, M.

    2001-01-01

    In this paper the large amplitude and non-linear vibration of a string is considered. The initial tension, lateral vibration amplitude, diameter and the modulus of elasticity of the string have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. In this case, therefore, it is impossible to use the classical equation of string with small amplitude transverse motion assumption. On the other hand, by increasing the string diameter, the bending moment effect will increase dramatically, and acts as an impressive restoring moment. Considering the effects of the bending moments, the nonlinear equation governing the large amplitude transverse vibration of a string is derived. The time dependent portion of the governing equation has the from of Duff ing equation is solved using the perturbation theory. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the string due to the non-linear factors are compared with the natural frequencies of the linear vibration os a string without bending moment effects

  18. Application of depletion perturbation theory to fuel cycle burnup analysis

    International Nuclear Information System (INIS)

    White, J.R.

    1979-01-01

    Over the past several years static perturbation theory methods have been increasingly used for reactor analysis in lieu of more detailed and costly direct computations. Recently, perturbation methods incorporating time dependence have also received attention, and several authors have demonstrated their applicability to fuel burnup analysis. The objective of the work described here is to demonstrate that a time-dependent perturbation method can be easily and accurately applied to realistic depletion problems

  19. Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

    Science.gov (United States)

    Kurashige, Yuki; Yanai, Takeshi

    2011-09-07

    We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

  20. Exact-to-precision generalized perturbation theory for source-driven systems

    International Nuclear Information System (INIS)

    Wang Congjian; Abdel-Khalik, Hany S.

    2011-01-01

    Highlights: ► We present a new development in higher order generalized perturbation theory. ► The method addresses the explosion in the flux phase space, input parameters, and responses. ► The method hybridizes first-order GPT and proper orthogonal decomposition snapshots method. ► A simplified 1D and realistic 2D assembly models demonstrate applicability of the method. ► The accuracy of the method is compared to exact direct perturbations and first-order GPT. - Abstract: Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.

  1. Time-Sliced Perturbation Theory II: Baryon Acoustic Oscillations and Infrared Resummation

    CERN Document Server

    Blas, Diego; Ivanov, Mikhail M.; Sibiryakov, Sergey

    2016-01-01

    We use time-sliced perturbation theory (TSPT) to give an accurate description of the infrared non-linear effects affecting the baryonic acoustic oscillations (BAO) present in the distribution of matter at very large scales. In TSPT this can be done via a systematic resummation that has a simple diagrammatic representation and does not involve uncontrollable approximations. We discuss the power counting rules and derive explicit expressions for the resummed matter power spectrum up to next-to leading order and the bispectrum at the leading order. The two-point correlation function agrees well with N-body data at BAO scales. The systematic approach also allows to reliably assess the shift of the baryon acoustic peak due to non-linear effects.

  2. Quenched Chiral Perturbation Theory to one loop

    NARCIS (Netherlands)

    Colangelo, G.; Pallante, E.

    The divergences of the generating functional of quenched Chiral Perturbation theory (qCHPT) to one loop are computed in closed form. We show how the quenched chiral logarithms can be reabsorbed in the renormalization of the B0 parameter of the leading order Lagrangian. Finally, we do the chiral

  3. On post-inflation validity of perturbation theory in Horndeski scalar-tensor models

    Energy Technology Data Exchange (ETDEWEB)

    Germani, Cristiano [Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí Franquès 1, E08028 Barcelona (Spain); Kudryashova, Nina [Arnold Sommerfeld Center, Ludwig-Maximilians-University, Theresienstr. 37, 80333 Muenchen (Germany); Watanabe, Yuki, E-mail: germani@icc.ub.edu, E-mail: nina.kudryashova@campus.lmu.de, E-mail: yuki.watanabe@nat.gunma-ct.ac.jp [Department of Physics, National Institute of Technology, Gunma College, Gunma 371-8530 (Japan)

    2016-08-01

    By using the newtonian gauge, we re-confirm that, as in the minimal case, the re-scaled Mukhanov-Sasaki variable is conserved leading to a constraint equation for the Newtonian potential. However, conversely to the minimal case, in Horndeski theories, the super-horizon Newtonian potential can potentially grow to very large values after inflation exit. If that happens, inflationary predictability is lost during the oscillating period. When this does not happen, the perturbations generated during inflation can be standardly related to the CMB, if the theory chosen is minimal at low energies. As a concrete example, we analytically and numerically discuss the new Higgs inflationary case. There, the Inflaton is the Higgs boson that is non-minimally kinetically coupled to gravity. During the high-energy part of the post-inflationary oscillations, the system is anisotropic and the Newtonian potential is largely amplified. Thanks to the smallness of today's amplitude of curvature perturbations, however, the system stays in the linear regime, so that inflationary predictions are not lost. At low energies, when the system relaxes to the minimal case, the anisotropies disappear and the Newtonian potential converges to a constant value. We show that the constant value to which the Newtonian potential converges is related to the frozen part of curvature perturbations during inflation, precisely like in the minimal case.

  4. Introduction to statistical field theory: from a toy model to a one-component plasma

    International Nuclear Information System (INIS)

    Frydel, Derek

    2015-01-01

    Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard–Stratonovich transformation). We then consider Gaussian-type approximations, wherein correlational contributions enter as harmonic fluctuations around the saddle-point solution. This work focuses on how to arrive at a self-consistent, non-perturbative approximation without recourse to a standard variational construction based on the Gibbs–Bogolyubov–Feynman inequality that is inapplicable to a complex action. To address this problem, we propose a construction based on selective satisfaction of a set of exact relations generated by considering a dual representation of a partition function, in its original and transformed form. (paper)

  5. Non-cyclic phases for neutrino oscillations in quantum field theory

    International Nuclear Information System (INIS)

    Blasone, Massimo; Capolupo, Antonio; Celeghini, Enrico; Vitiello, Giuseppe

    2009-01-01

    We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum field theory. Such phases carry information about the non-perturbative vacuum structure associated with the field mixing. By subtracting the condensate contribution of the flavor vacuum, the previously studied quantum mechanics geometric phase is recovered.

  6. A non-perturbative approach to strings

    International Nuclear Information System (INIS)

    Orland, P.

    1986-01-01

    After briefly reviewing the theory of strings in the light-cone gauge, a lattice regularized path integral for the amplitudes is discussed. The emphasis is put on a toy string model; the U(N) Veneziano model in the limit as N → ∞, with g/sup 2//sub o/N fixed. The lattice methods of Giles and Thorn are used extensively, but are found to require modification beyond perturbation theory. The twenty-six-dimensional toy string model is recast as a two-dimensional spin system

  7. Matrix models as non-commutative field theories on R3

    International Nuclear Information System (INIS)

    Livine, Etera R

    2009-01-01

    In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as generalized matrix models. Focusing on 2d group field theories, we review their explicit relation to matrix models and show their link to a class of non-commutative field theories invariant under a quantum-deformed 3d Poincare symmetry. This provides a simple relation between matrix models and non-commutative geometry. Moreover, we review the derivation of effective 2d group field theories with non-trivial propagators from Boulatov's group field theory for 3d quantum gravity. Besides the fact that this gives a simple and direct derivation of non-commutative field theories for the matter dynamics coupled to (3d) quantum gravity, these effective field theories can be expressed as multi-matrix models with a non-trivial coupling between matrices of different sizes. It should be interesting to analyze this new class of theories, both from the point of view of matrix models as integrable systems and for the study of non-commutative field theories.

  8. Cosmological perturbation theory at three-loop order

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-09-15

    We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

  9. Cosmological perturbation theory at three-loop order

    International Nuclear Information System (INIS)

    Blas, Diego; Garny, Mathias; Konstandin, Thomas

    2013-09-01

    We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

  10. A general-model-space diagrammatic perturbation theory

    International Nuclear Information System (INIS)

    Hose, G.; Kaldor, U.

    1980-01-01

    A diagrammatic many-body perturbation theory applicable to arbitrary model spaces is presented. The necessity of having a complete model space (all possible occupancies of the partially-filled shells) is avoided. This requirement may be troublesome for systems with several well-spaced open shells, such as most atomic and molecular excited states, as a complete model space spans a very broad energy range and leaves out states within that range, leading to poor or no convergence of the perturbation series. The method presented here would be particularly useful for such states. The solution of a model problem (He 2 excited Σ + sub(g) states) is demonstrated. (Auth.)

  11. A non-perturbative exploration of the high energy regime in Nf=3 QCD. ALPHA Collaboration

    Science.gov (United States)

    Dalla Brida, Mattia; Fritzsch, Patrick; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer

    2018-05-01

    Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schrödinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to implicitly define a reference scale 1/L_0≈ 4 GeV through \\bar{g}^2(L_0) =2.012, we quote L_0 Λ ^{N_f=3}_{{\\overline{MS}}} =0.0791(21). This error is dominated by statistics; in particular, the remnant perturbative uncertainty is negligible and very well controlled, by connecting to infinite renormalization scale from different scales 2^n/L_0 for n=0,1,\\ldots ,5. An intermediate step in this connection may involve any member of a one-parameter family of SF couplings. This provides an excellent opportunity for tests of perturbation theory some of which have been published in a letter (ALPHA collaboration, M. Dalla Brida et al. in Phys Rev Lett 117(18):182001, 2016). The results indicate that for our target precision of 3 per cent in L_0 Λ ^{N_f=3}_{{\\overline{MS}}}, a reliable estimate of the truncation error requires non-perturbative data for a sufficiently large range of values of α _s=\\bar{g}^2/(4π ). In the present work we reach this precision by studying scales that vary by a factor 2^5= 32, reaching down to α _s≈ 0.1. We here provide the details of our analysis and an extended discussion.

  12. Finite field-dependent symmetries in perturbative quantum gravity

    International Nuclear Information System (INIS)

    Upadhyay, Sudhaker

    2014-01-01

    In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also

  13. Effect of Hydrotherapy on Static and Dynamic Balance in Older Adults: Comparison of Perturbed and Non-Perturbed Programs

    Directory of Open Access Journals (Sweden)

    Elham Azimzadeh

    2013-01-01

    Full Text Available Objectives: Falling is a main cause of mortality in elderly. Balance training exercises can help to prevent falls in older adults. According to the principle of specificity of training, the perturbation-based trainings are more similar to the real world. So these training programs can improve balance in elderly. Furthermore, exercising in an aquatic environment can reduce the limitations for balance training rather than a non-aquatic on. The aim of this study is comparing the effectiveness of perturbed and non-perturbed balance training programs in water on static and dynamic balance in aforementioned population group. Methods & Materials: 37 old women (age 80-65, were randomized to the following groups: perturbation-based training (n=12, non-perturbation-based training (n=12 and control (n=13 groups. Static and dynamic balance had been tested before and after the eight weeks of training by the postural stability test of the Biodex balance system using dynamic (level 4 and static platform. The data were analyzed by one sample paired t-test, Independent t-test and ANOVA. Results: There was a significant improvement for all indexes of static and dynamic balance in perturbation-based training (P<0.05. However, in non-perturbed group, all indexes were improved except ML (P<0.05. ANOVA showed that perturbed training was more effective than non-perturbed training on both static and dynamic balances. Conclusion: The findings confirmed the specificity principle of training. Although balance training can improve balance abilities, these kinds of trainings are not such specific for improving balance neuromuscular activities.The perturbation-based trainings can activate postural compensatory responses and reduce falling risk. According to results, we can conclude that hydrotherapy especially with perturbation-based programs will be useful for rehabilitation interventions in elderly .

  14. Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study

    International Nuclear Information System (INIS)

    Bietenholz, W.; Bigarini, A.; INFN, Sezione di Perugia; Humboldt-Universitaet, Berlin; Torrielli, A.

    2007-06-01

    We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)

  15. Mass generation in perturbed massless integrable models

    International Nuclear Information System (INIS)

    Controzzi, D.; Mussardo, G.

    2005-01-01

    We extend form-factor perturbation theory to non-integrable deformations of massless integrable models, in order to address the problem of mass generation in such systems. With respect to the standard renormalisation group analysis this approach is more suitable for studying the particle content of the perturbed theory. Analogously to the massive case, interesting information can be obtained already at first order, such as the identification of the operators which create a mass gap and those which induce the confinement of the massless particles in the perturbed theory

  16. Scheme (in?) dependence in perturbative Lagrangian quantum field theory

    International Nuclear Information System (INIS)

    Slavnov, D.A.

    1995-01-01

    A problem of renormalization - scheme ambiguity in perturbation quantum field theory is investigated. A procedure is described that makes it possible to express uniquely all observable quantities in terms of a set base observables. Renormalization group equations for the base observable are constructed. The case of mass theory is treated. 9 refs

  17. Dimensional perturbation theory for the two-electron atom

    International Nuclear Information System (INIS)

    Goodson, D.Z.

    1987-01-01

    Perturbation theory in δ = 1/D, where D is the dimensionality of space, is applied to the two-electron atom. In Chapter 1 an efficient procedure for calculating the coefficients of the perturbation series for the ground-state energy is developed using recursion relations between the moments of the coordinate operators. Results through tenth order are presented. The series is divergent, but Pade summation gives results comparable in accuracy to the best configuration-interaction calculations. The singularity structure of the Pade approximants confirms the hypothesis that the energy as a function of δ has an infinite sequence of poles on the negative real axis that approaches an essential singularity at δ = O. The essential singularity causes the divergence of the perturbation series. There are also two poles at δ = 1 that slow the asymptotic convergence of the low-order terms. In Chapter 2, various techniques are demonstrated for removing the effect of these poles, and accurate results are thereby obtained, even at very low order. In Chapter 3, the large D limit of the correlation energy (CE) is investigated. In the limit D → infinity it is only 35% smaller than at D = 3. It can be made to vanish in the limit by modifying the Hartree-Fock (HF) wavefunction. In Chapter 4, perturbation theory is applied to the Hooke's-law model of the atom. Prospects for treating more-complicated systems are briefly discussed

  18. Quasipotential in the fourth order of perturbation theory

    International Nuclear Information System (INIS)

    Bojkova, N.A.; Dvoeglazov, V.V.; Tyukhtyaev, Yu.N.; Faustov, R.N.

    1992-01-01

    The quasipotential in the fourth order of perturbation theory is calculated in the Coulomb gauge for the unequal mass particles. It could be used for the future calculations of energy spectra in two-body systems. 15 refs.; 1 fig

  19. Proof of ultraviolet finiteness for a planar non-supersymmetric Yang-Mills theory

    International Nuclear Information System (INIS)

    Ananth, Sudarshan; Kovacs, Stefano; Shimada, Hidehiko

    2007-01-01

    This paper focuses on a three-parameter deformation of N=4 Yang-Mills that breaks all the supersymmetry in the theory. We show that the resulting non-supersymmetric gauge theory is scale invariant, in the planar approximation, by proving that its Green functions are ultraviolet finite to all orders in light-cone perturbation theory

  20. Generating scale-invariant tensor perturbations in the non-inflationary universe

    International Nuclear Information System (INIS)

    Li, Mingzhe

    2014-01-01

    It is believed that the recent detection of large tensor perturbations strongly favors the inflation scenario in the early universe. This common sense depends on the assumption that Einstein's general relativity is valid at the early universe. In this paper we show that nearly scale-invariant primordial tensor perturbations can be generated during a contracting phase before the radiation dominated epoch if the theory of gravity is modified by the scalar–tensor theory at that time. The scale-invariance protects the tensor perturbations from suppressing at large scales and they may have significant amplitudes to fit BICEP2's result. We construct a model to achieve this purpose and show that the universe can bounce to the hot big bang after long time contraction, and at almost the same time the theory of gravity approaches to general relativity through stabilizing the scalar field. Theoretically, such models are dual to inflation models if we change to the frame in which the theory of gravity is general relativity. Dual models are related by the conformal transformations. With this study we reinforce the point that only the conformal invariant quantities such as the scalar and tensor perturbations are physical. How did the background evolve before the radiation time depends on the frame and has no physical meaning. It is impossible to distinguish different pictures by later time cosmological probes.

  1. Generating scale-invariant tensor perturbations in the non-inflationary universe

    Directory of Open Access Journals (Sweden)

    Mingzhe Li

    2014-09-01

    Full Text Available It is believed that the recent detection of large tensor perturbations strongly favors the inflation scenario in the early universe. This common sense depends on the assumption that Einstein's general relativity is valid at the early universe. In this paper we show that nearly scale-invariant primordial tensor perturbations can be generated during a contracting phase before the radiation dominated epoch if the theory of gravity is modified by the scalar–tensor theory at that time. The scale-invariance protects the tensor perturbations from suppressing at large scales and they may have significant amplitudes to fit BICEP2's result. We construct a model to achieve this purpose and show that the universe can bounce to the hot big bang after long time contraction, and at almost the same time the theory of gravity approaches to general relativity through stabilizing the scalar field. Theoretically, such models are dual to inflation models if we change to the frame in which the theory of gravity is general relativity. Dual models are related by the conformal transformations. With this study we reinforce the point that only the conformal invariant quantities such as the scalar and tensor perturbations are physical. How did the background evolve before the radiation time depends on the frame and has no physical meaning. It is impossible to distinguish different pictures by later time cosmological probes.

  2. Application of generalized perturbation theory to flux disadvantage factor calculations

    International Nuclear Information System (INIS)

    Sallam, O.H.; Akimov, I.S.; Naguib, K.; Hamouda, I.

    1979-01-01

    The possibility of using the generalized perturbation theory to calculate the perturbation of the flux disadvantage factors of reactor cell, resulting from the variation of the cell parameters, is studied. For simplicity the one-group diffusion approximation is considered. All necessary equations are derived for variations both of the cell dimensions. Numerical results are presented in the paper

  3. Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions

    International Nuclear Information System (INIS)

    Ishikawa, Y.; Quiney, H.M.

    1993-01-01

    A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence

  4. Advances in heuristically based generalized perturbation theory

    International Nuclear Information System (INIS)

    Gandini, A.

    1994-01-01

    A distinctive feature of heuristically based generalized perturbation theory methodology consists in the systematic use of importance conservation concepts. As well known, this use leads to fundamental reciprocity relationship. Instead, the alternative variational and differential one approaches make a consistent use of the properties and adjoint functions. The equivalence between the importance and the adjoint functions have been demonstrated in important cases. There are some instances, however, in which the commonly known operator governing the adjoint function are not adequate. In this paper ways proposed to generalize this rules, as adopted with the heuristic generalized perturbation theory methodology, are illustrated. When applied to the neutron/nuclide field characterizing the core evolution in a power reactor system, in which also an intensive control variable (ρ) is defined, these rules leas to an orthogonality relationship connected to this same control variable. A set of ρ-mode eigenfunctions may be correspondingly defined and an extended concept of reactivity (generalizing that commonly associated with the multiplication factor) proposed as more directly indicative of the controllability of a critical reactor system. (author). 25 refs

  5. Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: theory and test calculations of second order approximation.

    Science.gov (United States)

    Chen, Zhenhua; Hoffmann, Mark R

    2012-07-07

    A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4

  6. The Operator Product Expansion Beyond Perturbation Theory in QCD

    International Nuclear Information System (INIS)

    Dominguez, C. A.

    2011-01-01

    The Operator Product Expansion (OPE) of current correlators at short distances beyond perturbation theory in QCD, together with Cauchy's theorem in the complex energy plane, are the pillars of the method of QCD sum rules. This technique provides an analytic tool to relate QCD with hadronic physics at low and intermediate energies. It has been in use for over thirty years to determine hadronic parameters, form factors, and QCD parameters such as the quark masses, and the running strong coupling at the scale of the τ-lepton. QCD sum rules provide a powerful complement to numerical simulations of QCD on the lattice. In this talk a short review of the method is presented for non experts, followed by three examples of recent applications.

  7. SMD-based numerical stochastic perturbation theory

    Science.gov (United States)

    Dalla Brida, Mattia; Lüscher, Martin

    2017-05-01

    The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.

  8. SMD-based numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Dalla Brida, Mattia [Universita di Milano-Bicocca, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano-Bicocca (Italy); Luescher, Martin [CERN, Theoretical Physics Department, Geneva (Switzerland); AEC, Institute for Theoretical Physics, University of Bern (Switzerland)

    2017-05-15

    The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)

  9. SMD-based numerical stochastic perturbation theory

    International Nuclear Information System (INIS)

    Dalla Brida, Mattia; Luescher, Martin

    2017-01-01

    The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)

  10. Perturbation theory for plasmonic modulation and sensing

    KAUST Repository

    Raman, Aaswath

    2011-05-25

    We develop a general perturbation theory to treat small parameter changes in dispersive plasmonic nanostructures and metamaterials. We specifically apply it to dielectric refractive index and metallic plasma frequency modulation in metal-dielectric nanostructures. As a numerical demonstration, we verify the theory\\'s accuracy against direct calculations for a system of plasmonic rods in air where the metal is defined by a three-pole fit of silver\\'s dielectric function. We also discuss new optical behavior related to plasma frequency modulation in such systems. Our approach provides new physical insight for the design of plasmonic devices for biochemical sensing and optical modulation and future active metamaterial applications. © 2011 American Physical Society.

  11. Perturbation theory of a symmetric center within Liénard equations

    Science.gov (United States)

    Françoise, Jean-Pierre; Xiao, Dongmei

    2015-09-01

    In this article, we introduce the use of Lambert function to develop further the global perturbation theory of an integrable Liénard equation which displays a symmetric center. We prove a global Morse lemma for the first integral and deduce the existence of an associated Picard-Fuchs system. We revisit previous contributions to first-order perturbation theory with the help of these new analytic techniques and in particular, we check that the fundamental integrals are linearly independent. The Lambert function allows to find an expansion formula for these integrals. We also study the possibility to develop a higher-order perturbation theory. The algorithm of the successive derivatives works in general in the class of analytic functions on the domain D where the level sets of the first integral are ovals. We end the article with some results on the first integral of a symmetric Liénard equation deduced from the algorithm of successive derivatives.

  12. Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

    International Nuclear Information System (INIS)

    Marcos, B.

    2008-01-01

    Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.

  13. Chiral perturbation theory for nucleon generalized parton distributions

    Energy Technology Data Exchange (ETDEWEB)

    Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Manashov, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik]|[Sankt-Petersburg State Univ. (Russian Federation). Dept. of Theoretical Physics; Schaefer, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik

    2006-08-15

    We analyze the moments of the isosinglet generalized parton distributions H, E, H, E of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit. (orig.)

  14. Statistical mechanics view of quantum chromodynamics: Lattice gauge theory

    International Nuclear Information System (INIS)

    Kogut, J.B.

    1984-01-01

    Recent developments in lattice gauge theory are discussed from a statistial mechanics viewpoint. The basic physics problems of quantum chromodynamics (QCD) are reviewed for an audience of critical phenomena theorists. The idea of local gauge symmetry and color, the connection between statistical mechanics and field theory, asymptotic freedom and the continuum limit of lattice gauge theories, and the order parameters (confinement and chiral symmetry) of QCD are reviewed. Then recent developments in the field are discussed. These include the proof of confinement in the lattice theory, numerical evidence for confinement in the continuum limit of lattice gauge theory, and perturbative improvement programs for lattice actions. Next, we turn to the new challenges facing the subject. These include the need for a better understanding of the lattice Dirac equation and recent progress in the development of numerical methods for fermions (the pseudofermion stochastic algorithm and the microcanonical, molecular dynamics equation of motion approach). Finally, some of the applications of lattice gauge theory to QCD spectrum calculations and the thermodynamics of QCD will be discussed and a few remarks concerning future directions of the field will be made

  15. {alpha}{sub s} from the non-perturbatively renormalised lattice three-gluon vertex

    Energy Technology Data Exchange (ETDEWEB)

    Alles, B. [Pisa Univ. (Italy). Dipt. di Fisica; Henty, D.S. [Department of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ (United Kingdom); Panagopoulos, H. [Department of Natural Sciences, University of Cyprus, CY-1678 Nicosia (Cyprus); Parrinello, C. [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX (United Kingdom); Pittori, C. [L.P.T.H.E., Universite de Paris Sud, Centre d`Orsay, 91405 Orsay (France); Richards, D.G. [Department of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ (United Kingdom)]|[Fermilab, P.O. Box 500, Batavia, IL 60510 (United States)

    1997-09-29

    We compute the running QCD coupling on the lattice by evaluating two-point and three-point off-shell gluon Green`s functions in a fixed gauge and imposing non-perturbative renormalisation conditions on them. Our exploratory study is performed in the quenched approximation at {beta}=6.0 on 16{sup 4} and 24{sup 4} lattices. We show that, for momenta in the range 1.8-2.3 GeV, our coupling runs according to the two-loop asymptotic formula, allowing a precise determination of the corresponding {Lambda} parameter. The role of lattice artifacts and finite-volume effects is carefully analysed and these appear to be under control in the momentum range of interest. Our renormalisation procedure corresponds to a momentum subtraction scheme in continuum field theory, and therefore lattice perturbation theory is not needed in order to match our results to the anti M anti S scheme, thus eliminating a major source of uncertainty in the determination of {alpha} {sub anti} {sub M} {sub anti} {sub S}. Our method can be applied directly to the unquenched case. (orig.). 20 refs.

  16. Inflation from Asymptotically Safe Theories

    DEFF Research Database (Denmark)

    Nielsen, Niklas Grønlund; Sannino, Francesco; Svendsen, Ole

    2015-01-01

    for inflation. In the minimal coupling case the theory requires large non-perturbative quantum corrections to the quantum potential for the theory to agree with data, while in the non- minimal coupling case the perturbative regime in the couplings of the theory is preferred. Requiring the theory to reproduce...... the observed amplitude of density perturbations constrain the geometric data of the theory such as the number of colors and flavors for generic values of the non-minimal coupling....

  17. Non-perturbative methods applied to multiphoton ionization

    International Nuclear Information System (INIS)

    Brandi, H.S.; Davidovich, L.; Zagury, N.

    1982-09-01

    The use of non-perturbative methods in the treatment of atomic ionization is discussed. Particular attention is given to schemes of the type proposed by Keldysh where multiphoton ionization and tunnel auto-ionization occur for high intensity fields. These methods are shown to correspond to a certain type of expansion of the T-matrix in the intra-atomic potential; in this manner a criterium concerning the range of application of these non-perturbative schemes is suggested. A brief comparison between the ionization rate of atoms in the presence of linearly and circularly polarized light is presented. (Author) [pt

  18. Development of a sensitivity analysis systems in nuclear reactors through generalized perturbation theory at first order in 2 D geometries

    International Nuclear Information System (INIS)

    Garcia, Juan Matias

    2005-01-01

    Perturbation Methods represent a powerful tool to do sensitivity analysis, and they found many aplications in nuclear engineering.As an introduction to this kind of analysis, we develope a program that apply the Generalized Perturbation Theory or GPT Method to bidimensional system of rectangular geometry.We first consider an homogeneous system of non-multiplying material and then an heterogeneous system with region of multiplying material, with the intention of make concret aplications of perturbation method to nuclear engineering problems.The program, that we called Pert, determines neutron fluxes and importance functions applying the Multigroup Diffusion Theory; and also solves the integrals required to calculate sensitivity coefficients.Using this perturbation methods we could verify the low computational cost required to make this kind of analysis and the simplicity of the equations systems involved, allowing us to make elaborates sensitivity analysis for the responses of our interest

  19. Perturbation theory for Markov chains via Wasserstein distance

    NARCIS (Netherlands)

    Rudolf, Daniel; Schweizer, Nikolaus

    2017-01-01

    Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the nth step distributions of two Markov chains

  20. Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion

    International Nuclear Information System (INIS)

    Tatekawa, Takayuki; Suda, Momoko; Maeda, Kei-ichi; Morita, Masaaki; Anzai, Hiroki

    2002-01-01

    We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This perturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of the inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in a wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein-de Sitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions, we present illustrative examples of our formulation in one- and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index

  1. Thoughts on non-perturbative thermalization and jet quenching in heavy ion collisions

    International Nuclear Information System (INIS)

    Kovchegov, Yuri V.

    2006-01-01

    We start by presenting physical arguments for the impossibility of perturbative thermalization leading to (non-viscous) Bjorken hydrodynamic description of heavy ion collisions. These arguments are complimentary to our more formal argument presented in [Yu.V. Kovchegov, hep-ph/0503038]. We argue that the success of hydrodynamic models in describing the quark-gluon system produced in heavy ion collisions could only be due to non-perturbative strong coupling effects. We continue by studying non-perturbative effects in heavy ion collisions at high energies. We model non-perturbative phenomena by an instanton ensemble. We show that non-perturbative instanton vacuum fields may significantly contribute to jet quenching in nuclear collisions. At the same time, the instanton ensemble contribution to thermalization is likely to be rather weak, leading to non-perturbative thermalization time comparable to the time of hadronization. This example illustrates that jet quenching is not necessarily a signal of a thermalized medium. Indeed, since the instanton models do not capture all the effects of QCD vacuum (e.g., they do not account for confinement), there may be other non-perturbative effects facilitating thermalization of the system

  2. Recent Developments in Non-Fermi Liquid Theory

    Science.gov (United States)

    Lee, Sung-Sik

    2018-03-01

    Non-Fermi liquids are unconventional metals whose physical properties deviate qualitatively from those of noninteracting fermions due to strong quantum fluctuations near Fermi surfaces. They arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticles, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. However, it has been difficult to understand their universal low-energy physics due to a lack of theoretical methods that take into account strong quantum fluctuations in the presence of abundant low-energy degrees of freedom. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the codimension of Fermi surface. The second is a nonperturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.

  3. Entanglement entropy of non-unitary integrable quantum field theory

    Directory of Open Access Journals (Sweden)

    Davide Bianchini

    2015-07-01

    Full Text Available In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee–Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by ceff3log⁡ℓ where ceff is the effective central charge of the theory (a positive number related to the central charge and ℓ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum, it appears to be much more model-dependent for non-unitary models.

  4. Multireference second order perturbation theory with a simplified treatment of dynamical correlation.

    Science.gov (United States)

    Xu, Enhua; Zhao, Dongbo; Li, Shuhua

    2015-10-13

    A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.

  5. The cosmological perturbation theory in loop cosmology with holonomy corrections

    International Nuclear Information System (INIS)

    Wu, Jian-Pin; Ling, Yi

    2010-01-01

    In this paper we investigate the scalar mode of first-order metric perturbations over spatially flat FRW spacetime when the holonomy correction is taken into account in the semi-classical framework of loop quantum cosmology. By means of the Hamiltonian derivation, the cosmological perturbation equations is obtained in longitudinal gauge. It turns out that in the presence of metric perturbation the holonomy effects influence both background and perturbations, and contribute the non-trivial terms S h1 and S h2 in the cosmological perturbation equations

  6. A Theory of the Perturbed Consumer with General Budgets

    DEFF Research Database (Denmark)

    McFadden, Daniel L; Fosgerau, Mogens

    We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose...... subgradients with respect to these perturbations are convex hulls of the utility-maximizing demands. We give necessary as well as sufficient conditions for DGF to be consistent with utility maximization, and establish under quite general conditions that utility-maximizing demands are almost everywhere single......-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints....

  7. The precession of mercury's perihelion via perturbation theory

    International Nuclear Information System (INIS)

    Rosales, M.H.; Castro-Quilantan, J.L.

    1984-01-01

    Perturbation theory is used to solve the problem of the precession of Mercury's perihelion, this phenomenon being a relativistic effect. The expansion parameter appears naturally when the orbit equation is written in an appropriate form and it completely justifies the use of the first order approximation. (author)

  8. A non-perturbative operator product expansion

    International Nuclear Information System (INIS)

    Bietenholz, W.; Cundy, N.; Goeckeler, M.

    2009-10-01

    Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photonmomenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This overdetermines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition. (orig.)

  9. Non-perturbative inputs for gluon distributions in the hadrons

    International Nuclear Information System (INIS)

    Ermolaev, B.I.; Troyan, S.I.

    2017-01-01

    Description of hadronic reactions at high energies is conventionally done in the framework of QCD factorization. All factorization convolutions comprise non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct inputs for the gluon-hadron scattering amplitudes in the forward kinematics and, using the optical theorem, convert them into inputs for gluon distributions in the hadrons, embracing the cases of polarized and unpolarized hadrons. In the first place, we formulate mathematical criteria which any model for the inputs should obey and then suggest a model satisfying those criteria. This model is based on a simple reasoning: after emitting an active parton off the hadron, the remaining set of spectators becomes unstable and therefore it can be described through factors of the resonance type, so we call it the resonance model. We use it to obtain non-perturbative inputs for gluon distributions in unpolarized and polarized hadrons for all available types of QCD factorization: basic, K_T-and collinear factorizations. (orig.)

  10. Non-perturbative inputs for gluon distributions in the hadrons

    Energy Technology Data Exchange (ETDEWEB)

    Ermolaev, B.I. [Ioffe Physico-Technical Institute, Saint Petersburg (Russian Federation); Troyan, S.I. [St. Petersburg Institute of Nuclear Physics, Gatchina (Russian Federation)

    2017-03-15

    Description of hadronic reactions at high energies is conventionally done in the framework of QCD factorization. All factorization convolutions comprise non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct inputs for the gluon-hadron scattering amplitudes in the forward kinematics and, using the optical theorem, convert them into inputs for gluon distributions in the hadrons, embracing the cases of polarized and unpolarized hadrons. In the first place, we formulate mathematical criteria which any model for the inputs should obey and then suggest a model satisfying those criteria. This model is based on a simple reasoning: after emitting an active parton off the hadron, the remaining set of spectators becomes unstable and therefore it can be described through factors of the resonance type, so we call it the resonance model. We use it to obtain non-perturbative inputs for gluon distributions in unpolarized and polarized hadrons for all available types of QCD factorization: basic, K{sub T}-and collinear factorizations. (orig.)

  11. Introduction to nonequilibrium statistical mechanics with quantum field theory

    International Nuclear Information System (INIS)

    Kita, Takafumi

    2010-01-01

    In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (1) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (2) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (3) to derive an expression of nonequilibrium entropy that evolves with time. In stage (1), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Φ-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Φ-derivable approximation, i.e., an issue of how to handle the 'Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy'. Aim (2) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems can be handled microscopically with

  12. Holographic stress tensor for non-relativistic theories

    International Nuclear Information System (INIS)

    Ross, Simon F.; Saremi, Omid

    2009-01-01

    We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.

  13. Non-perturbative treatment of excitation and ionization in U92++U91+ collisions at 1 GeV/amu

    International Nuclear Information System (INIS)

    Becker, U.; Gruen, N.; Scheid, W.; Soff, G.

    1986-01-01

    Inner shell excitation and ionization processes in relativistic collisions of very heavy ions are treated by a non-perturbative method for the first time. The time-dependent Dirac equation is solved by a finite difference method for the scattering of U 92+ on U 91+ at Esub(lab) = 1 GeV/amu and zero impact parameter. The K-shell ionization probabilities are compared with those resulting from first-order perturbation theory. (orig.)

  14. Existence of localizing solutions in plasticity via the geometric singular perturbation theory

    KAUST Repository

    Lee, Min-Gi; Tzavaras, Athanasios

    2017-01-01

    system has fast and slow time scales, forming a singularly perturbed problem. Geometric singular perturbation theory is applied to this problem to achieve an invariant surface. The flow on the invariant surface is analyzed via the Poincaré

  15. Non-Markovian linear response theory for quantum open systems and its applications.

    Science.gov (United States)

    Shen, H Z; Li, D X; Yi, X X

    2017-01-01

    The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.

  16. A strategy for implementing non-perturbative renormalisation of heavy-light four-quark operators in the static approximation

    Energy Technology Data Exchange (ETDEWEB)

    Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Papinutto, M. [Istituto Nazionale di Fisica Nucleare, Rome (Italy); Pena, C. [European Organization for Nuclear Research, Geneva (Switzerland). Theoretical Physics Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik

    2006-04-15

    We discuss the renormalisation properties of the complete set of {delta}B=2 four-quark operators with the heavy quark treated in the static approximation. We elucidate the role of heavy quark symmetry and other symmetry transformations in constraining their mixing under renormalisation. By employing the Schroedinger functional, a set of non-perturbative renormalisation conditions can be defined in terms of suitable correlation functions. As a first step in a fully non-perturbative determination of the scale-dependent renormalisation factors, we evaluate these conditions in lattice perturbation theory at one loop. Thereby we verify the expected mixing patterns and determine the anomalous dimensions of the operators at NLO in the Schroedinger functional scheme. Finally, by employing twisted-mass QCD it is shown how finite subtractions arising from explicit chiral symmetry breaking can be avoided completely. (Orig.)

  17. A strategy for implementing non-perturbative renormalisation of heavy-light four-quark operators in the static approximation

    International Nuclear Information System (INIS)

    Palombi, F.; Pena, C.; Wittig, H.

    2006-04-01

    We discuss the renormalisation properties of the complete set of ΔB=2 four-quark operators with the heavy quark treated in the static approximation. We elucidate the role of heavy quark symmetry and other symmetry transformations in constraining their mixing under renormalisation. By employing the Schroedinger functional, a set of non-perturbative renormalisation conditions can be defined in terms of suitable correlation functions. As a first step in a fully non-perturbative determination of the scale-dependent renormalisation factors, we evaluate these conditions in lattice perturbation theory at one loop. Thereby we verify the expected mixing patterns and determine the anomalous dimensions of the operators at NLO in the Schroedinger functional scheme. Finally, by employing twisted-mass QCD it is shown how finite subtractions arising from explicit chiral symmetry breaking can be avoided completely. (Orig.)

  18. Contribution of higher order terms in the reductive perturbation theory, 2

    International Nuclear Information System (INIS)

    Ichikawa, Y.H.; Mitsuhashi, Teruo; Konno, Kimiaki.

    1977-01-01

    Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schroedinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically in the asymptotic limit of small wave number. (auth.)

  19. Lattice field theories: non-perturbative methods of analysis

    International Nuclear Information System (INIS)

    Weinstein, M.

    1978-01-01

    A lecture is given on the possible extraction of interesting physical information from quantum field theories by studying their semiclassical versions. From the beginning the problem of solving for the spectrum states of any given continuum quantum field theory is considered as a giant Schroedinger problem, and then some nonperturbative methods for diagonalizing the Hamiltonian of the theory are explained without recourse to semiclassical approximations. The notion of a lattice appears as an artifice to handle the problems associated with the familiar infrared and ultraviolet divergences of continuum quantum field theory and in fact for all but gauge theories. 18 references

  20. Non-leading contributions in QCD: Summing the perturbative series

    International Nuclear Information System (INIS)

    Trentadue, L.

    1984-01-01

    This paper presents the results of a systematic analysis of the leading and non-leading contributions in perturbative QCD and addresses the question of logarithmic contributions to all orders of the perturbative series

  1. The SU(3) beta function from numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Bonn Univ. (Germany). Helmholtz Inst. fuer Strahlen- und Kernphysik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G.; Schiller, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-09-15

    The SU(3) beta function is derived from Wilson loops computed to 20th order in numerical stochastic perturbation theory. An attempt is made to include massless fermions, whose contribution is known analytically to 4th order. The question whether the theory admits an infrared stable fixed point is addressed.

  2. Orbital classical solutions, non-perturbative phenomena and singularity at the zero coupling constant point

    International Nuclear Information System (INIS)

    Vourdas, A.

    1982-01-01

    We try to extend previous arguments on orbital classical solutions in non-relativistic quantum mechanics to the 1/4lambda vertical stroke phi vertical stroke 4 complex relativistic field theory. The single valuedness of the Green function in the semiclassical (Planksche Konstante → 0) limit leads to a Bohr-Sommerfeld quantization. A path integral formalism for the Green functions analogous to that in non-relativistic quantum mechanics is employed and a semiclassical approach which uses our classical solutions indicates non-perturbative effects. They reflect an esub(1/lambda) singularity at the zero coupling constant point. (orig.)

  3. Keldysh meets Lindblad: Correlated Gain and Loss in Higher Order Perturbation Theory

    Science.gov (United States)

    Stace, Tom; Mueller, Clemens

    Motivated by correlated decay processes driving gain, loss and lasing in driven artificial quantum systems, we develop a theoretical technique using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behaviour at the same order of perturbation theory. We then apply these results to analyse the phonon-assisted steady-state gain of a microwave field driving a double quantum-dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing- assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.

  4. How to make thermodynamic perturbation theory to be suitable for low temperature?

    Science.gov (United States)

    Zhou, Shiqi

    2009-02-07

    Low temperature unsuitability is a problem plaguing thermodynamic perturbation theory (TPT) for years. Present investigation indicates that the low temperature predicament can be overcome by employing as reference system a nonhard sphere potential which incorporates one part of the attractive ingredient in a potential function of interest. In combination with a recently proposed TPT [S. Zhou, J. Chem. Phys. 125, 144518 (2006)] based on a lambda expansion (lambda being coupling parameter), the new perturbation strategy is employed to predict for several model potentials. It is shown that the new perturbation strategy can very accurately predict various thermodynamic properties even if the potential range is extremely short and hence the temperature of interest is very low and current theoretical formalisms seriously deteriorate or critically fail to predict even the existence of the critical point. Extensive comparison with existing liquid state theories and available computer simulation data discloses a superiority of the present TPT to two Ornstein-Zernike-type integral equation theories, i.e., hierarchical reference theory and self-consistent Ornstein-Zernike approximation.

  5. Convergence and analytic properties of manifestly finite perturbation theory

    International Nuclear Information System (INIS)

    Mtingwa, S.K.

    1979-01-01

    The author discusses more carefully the ultraviolet convergence properties of Feynman diagrams in recently proposed manifestly finite perturbation expansions. Speccifically, he refines one of the constraints on the γ's-the noncanonical dimensions-such that, when satisfied, any general product-type interaction of massive scalar, fermion and vector fields yields finite perturbation expansions requiring no conventional renormalization procedure. Moreover, the analytic properties of the Feynman integrals in the theory are discussed and concluded with remarks on the necessity of a modified Kaellen-Lehmann representation

  6. Baryon form factors in chiral perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Kubis, B.; Meissner, U.G. [Forschungszentrum Juelich GmbH (Germany). Inst. fuer Kernphysik

    2001-01-01

    We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the {sigma}{sup -} charge radius and the {lambda}-{sigma}{sup 0} transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory. (orig.)

  7. Perturbation theory for Alfven wave

    International Nuclear Information System (INIS)

    Yoshida, Z.; Mahajan, S.M.

    1995-01-01

    The Alfven wave is the dominant low frequency transverse mode of a magnetized plasma. The Alfven wave propagation along the magnetic field, and displays a continuous spectrum even in a bounded plasma. This is essentially due to the degeneracy of the wave characteristics, i.e. the frequency (ω) is primarily determined by the wave number in the direction parallel to the ambient magnetic field (k parallel ) and is independent of the perpendicular wavenumbers. The characteristics, that are the direction along which the wave energy propagates, are identical to the ambient magnetic field lines. Therefore, the spectral structure of the Alfven wave has a close relationship with the geometric structure of the magnetic field lines. In an inhomogeneous plasma, the Alfven resonance constitutes a singularity for the defining wave equation; this results in a singular eigenfunction corresponding to the continuous spectrum. The aim of this review is to present an overview of the perturbation theory for the Alfven wave. Emphasis is placed on those perturbations of the continuous spectrum which lead to the creation of point spectra. Such qualitative changes in the spectrum are relevant to many plasma phenomena

  8. Development of New Open-Shell Perturbation and Coupled-Cluster Theories Based on Symmetric Spin Orbitals

    Science.gov (United States)

    Lee, Timothy J.; Arnold, James O. (Technical Monitor)

    1994-01-01

    A new spin orbital basis is employed in the development of efficient open-shell coupled-cluster and perturbation theories that are based on a restricted Hartree-Fock (RHF) reference function. The spin orbital basis differs from the standard one in the spin functions that are associated with the singly occupied spatial orbital. The occupied orbital (in the spin orbital basis) is assigned the delta(+) = 1/square root of 2(alpha+Beta) spin function while the unoccupied orbital is assigned the delta(-) = 1/square root of 2(alpha-Beta) spin function. The doubly occupied and unoccupied orbitals (in the reference function) are assigned the standard alpha and Beta spin functions. The coupled-cluster and perturbation theory wave functions based on this set of "symmetric spin orbitals" exhibit much more symmetry than those based on the standard spin orbital basis. This, together with interacting space arguments, leads to a dramatic reduction in the computational cost for both coupled-cluster and perturbation theory. Additionally, perturbation theory based on "symmetric spin orbitals" obeys Brillouin's theorem provided that spin and spatial excitations are both considered. Other properties of the coupled-cluster and perturbation theory wave functions and models will be discussed.

  9. Strong coupling effects in non-commutative spaces from OM theory and supergravity

    International Nuclear Information System (INIS)

    Russo, J.G.; Sheikh-Jabbari, M.M.

    2000-11-01

    We show that a four-parameter class of 3+1 dimensional NCOS theories can be obtained by dimensional reduction on a general 2-torus from OM theory. Compactifying two spatial directions of NCOS theory on a 2-torus, we study the transformation properties under the SO(2,2; Z) T-duality group. We then discuss non-perturbative configurations of non-commutative super Yang-Mills theory. In particular, we calculate the tension for magnetic monopoles and (p,q) dyons and exhibit their six-dimensional origin, and construct a supergravity solution representing an instanton in the gauge theory. We also compute the potential for a monopole-antimonopole in the supergravity approximation. (author)

  10. Non-perturbative QCD Effect on K-Factor of Drell-Yan Process

    International Nuclear Information System (INIS)

    Hou Zhaoyu; Zhi Haisu; Chen Junxiao

    2006-01-01

    By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative effect to K-factor of the Drell-Yan process is numerically investigated for 12 6 C- 12 6 C collision at the center-of-mass energy (s) 1/2 = 200 GeV, 630 GeV respectively. Calculated results show that the non-perturbative QCD effect has just a weak influence on K-factor in the two cases.

  11. Three-nucleon scattering by using chiral perturbation theory potential

    International Nuclear Information System (INIS)

    Kamata, Hiroyuki

    2003-01-01

    Three-nucleon scattering problems are studied by using two-nucleon and three-nucleon potentials derived from chiral perturbation theory. The three-nucleon term is shown to appear in the effective potential of the rank of next-to-next-to-leading order (NNLO). New three-nucleon forces are taken into consideration in addition to the conventional Fujita-Miyazawa (FM) type three-nucleon potential. Two-nucleon potential of the chiral perturbation theory is as precise as the conventional ones in low energy region. The FM type three-nucleon force which explains Sagara discrepancy in high energy region is introduced automatically. Concerning the Ay puzzle, the results seems to behave as if the puzzle has been solved at the level of NLO, but at the NNLO (without three-nucleon force) level the result is similar to the cases of conventional potential indicating the need of three-nucleon force. In contrast to the FM type three-nucleon force, five free parameters exist in the new D and E type three-nucleon forces introduced by the NNLO, but they are reduced to two independent parameters by antisymmetrization, which are found to be sensitive to the coupling energy of tritons and to the nd scattering length (spin doublet state). Parameters determined from them cannot give satisfactory answer to the A y puzzle. It seems, however, too hasty to conclude that A y puzzle cannot be solved by the chiral perturbation theory. (S. Funahashi)

  12. Renormalized perturbation theory: Vlasov-Poisson System, weak turbulence limit and gyrokinetics

    International Nuclear Information System (INIS)

    Zhang, Y.Z.; Mahajan, S.M.

    1987-10-01

    The Self-consistency of the renormalized perturbation theory is demonstrated by applying it to the Vlasov-Poisson System and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-β gyrokinetic system. Comparison of our theory with other current theories is presented. 22 refs

  13. Statistical mechanics, gravity, and Euclidean theory

    International Nuclear Information System (INIS)

    Fursaev, Dmitri V.

    2002-01-01

    A review of computations of free energy for Gibbs states on stationary but not static gravitational and gauge backgrounds is given. On these backgrounds wave equations for free fields are reduced to eigenvalue problems which depend non-linearly on the spectral parameter. We present a method to deal with such problems. In particular, we demonstrate how some results of the spectral theory of second-order elliptic operators, such as heat kernel asymptotics, can be extended to a class of non-linear spectral problems. The method is used to trace down the relation between the canonical definition of the free energy based on summation over the modes and the covariant definition given in Euclidean quantum gravity. As an application, high-temperature asymptotics of the free energy and of the thermal part of the stress-energy tensor in the presence of rotation are derived. We also discuss statistical mechanics in the presence of Killing horizons where canonical and Euclidean theories are related in a non-trivial way

  14. Nucleon and delta masses in twisted mass chiral perturbation theory

    International Nuclear Information System (INIS)

    Walker-Loud, Andre; Wu, Jackson M.S.

    2005-01-01

    We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing, a, and the quark masses, m q , to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We show that the mass splitting between the degenerate pairs of the deltas first appears at quadratic order in the lattice spacing. We discuss the subtleties in the effective chiral theory that arise from the inclusion of isospin breaking

  15. An Introduction to Perturbative Methods in Gauge Theories

    International Nuclear Information System (INIS)

    T Muta

    1998-01-01

    This volume develops the techniques of perturbative QCD in great pedagogical detail starting with field theory. Aside from extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions, this book provides a comprehensive introduction to gauge theories. Examples and exercises are provided to amplify the discussions on important topics. This is an ideal textbook on the subject of quantum chromodynamics and is essential for researchers and graduate students in high energy physics, nuclear physics and mathematical physics

  16. Introductory statistics for business and economics theory, exercises and solutions

    CERN Document Server

    Ubøe, Jan

    2017-01-01

    This textbook discusses central statistical concepts and their use in business and economics. To endure the hardship of abstract statistical thinking, business and economics students need to see interesting applications at an early stage. Accordingly, the book predominantly focuses on exercises, several of which draw on simple applications of non-linear theory. The main body presents central ideas in a simple, straightforward manner; the exposition is concise, without sacrificing rigor.  The book bridges the gap between theory and applications, with most exercises formulated in an economic context. Its simplicity of style makes the book suitable for students at any level, and every chapter starts out with simple problems. Several exercises, however, are more challenging, as they are devoted to the discussion of non-trivial economic problems where statistics plays a central part.

  17. R 2 inflation to probe non-perturbative quantum gravity

    Science.gov (United States)

    Koshelev, Alexey S.; Sravan Kumar, K.; Starobinsky, Alexei A.

    2018-03-01

    It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, R + R 2, or shortly R 2, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R 2 model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index ( n s ), a tensor-to-scalar ratio ( r) and a tensor tilt ( n t ). It appears that n s remains the same as in the local R 2 inflation in the leading slow-roll approximation, while r and n t get modified due to modification of the tensor power spectrum. This class of models allows for any value of r complete R 2 gravity a natural target for future CMB probes.

  18. The Schroedinger equation and canonical perturbation theory

    International Nuclear Information System (INIS)

    Graffi, S.; Paul, T.

    1987-01-01

    Let T 0 (ℎ,ω)+εV be the Schroedinger operator corresponding to the classical Hamiltonian H 0 (ω)+εV, where H 0 (ω) is the d-dimensional harmonic oscillator with non-resonant frequencies ω=(ω 1 ..., ω d ) and the potential V(q 1 , ..., q d ) is an entire function of order (d+l) -1 . We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schroedinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schroedinger series near any eigenvalue of T 0 (ℎ,ω) admits a convergent expansion in powers of ℎ of initial point the corresponding term of the classical Birkhoff expansion. Moreover if V is an even polynomial, the above result and the KAM theorem show that all eigenvalues λ n (ℎ,ε) of T 0 +εV such that nℎ coincides with a KAM torus are given, up to order ε ∞ , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in ℎ. (orig.)

  19. Electromagnetic couplings of the chiral perturbation theory Lagrangian from the perturbative chiral quark model

    International Nuclear Information System (INIS)

    Lyubovitskij, V.E.; Gutsche, Th.; Faessler, Amand; Mau, R. Vinh

    2002-01-01

    We apply the perturbative chiral quark model to the study of the low-energy πN interaction. Using an effective chiral Lagrangian we reproduce the Weinberg-Tomozawa result for the S-wave πN scattering lengths. After inclusion of the photon field we give predictions for the electromagnetic O(p 2 ) low-energy couplings of the chiral perturbation theory effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e 2 ) radiative corrections to the πN scattering amplitude. Finally, we estimate the leading isospin-breaking correction to the strong energy shift of the π - p atom in the 1s state, which is relevant for the experiment 'pionic hydrogen' at PSI

  20. Variational configuration interaction methods and comparison with perturbation theory

    International Nuclear Information System (INIS)

    Pople, J.A.; Seeger, R.; Krishnan, R.

    1977-01-01

    A configuration interaction (CI) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Moller-Plesset perturbation results to second and third order are obtained in the first CI iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final CI energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these CI methods with perturbation theory

  1. A higher order depletion perturbation theory with application to in-core fuel management optimization

    International Nuclear Information System (INIS)

    Kropaczek, D.J.; Turinsky, P.J.

    1990-01-01

    Perturbation techniques utilized in reactor analysis have recently been applied in the solution of the in-core nuclear fuel management optimization problem. The use of such methods is motivated by the need to evaluate many times over, the core physics characteristics of loading pattern solutions obtained through an optimization process, which is typically iterative. Perturbation theory provides an efficient alternative to the prohibitively expensive, repetitive solutions of the system few-group neutron diffusion equations required in solving the fuel placement problem. A primary concern in the use of such methods is the control of perturbation errors arising during the fuel shuffling process. First-order accurate models inevitably resort to undue restriction of fuel movement during the optimization process to control these errors. Higher order perturbation theory models have the potential to overcome such limitations, which may result in the identification of local versus global optima. An accurate, computationally efficient reactor physics model based on higher order perturbation theory and geared toward the needs of large-scale in-core fuel management optimization is presented in this paper

  2. Inflationary perturbations in no-scale theories

    Energy Technology Data Exchange (ETDEWEB)

    Salvio, Alberto [CERN, Theoretical Physics Department, Geneva (Switzerland)

    2017-04-15

    We study the inflationary perturbations in general (classically) scale-invariant theories. Such scenario is motivated by the hierarchy problem and provides natural inflationary potentials and dark matter candidates. We analyse in detail all sectors (the scalar, vector and tensor perturbations) giving general formulae for the potentially observable power spectra, as well as for the curvature spectral index n{sub s} and the tensor-to-scalar ratio r. We show that the conserved Hamiltonian for all perturbations does not feature negative energies even in the presence of the Weyl-squared term if the appropriate quantisation is performed and argue that this term does not lead to phenomenological problems at least in some relevant setups. The general formulae are then applied to a concrete no-scale model, which includes the Higgs and a scalar, ''the planckion'', whose vacuum expectation value generates the Planck mass. Inflation can be triggered by a combination of the planckion and the Starobinsky scalar and we show that no tension with observations is present even in the case of pure planckion inflation, if the coefficient of the Weyl-squared term is large enough. In general, even quadratic inflation is allowed in this case. Moreover, the Weyl-squared term leads to an isocurvature mode, which currently satisfies the observational bounds, but it may be detectable with future experiments. (orig.)

  3. Theoretical investigation of cyromazine tautomerism using density functional theory and Møller–Plesset perturbation theory methods

    Science.gov (United States)

    A computational chemistry analysis of six unique tautomers of cyromazine, a pesticide used for fly control, was performed with density functional theory (DFT) and canonical second order Møller–Plesset perturbation theory (MP2) methods to gain insight into the contributions of molecular structure to ...

  4. Linear theory of density perturbations in a neutrino+baryon universe

    International Nuclear Information System (INIS)

    Wasserman, I.

    1981-01-01

    Various aspects of the linear theory of density perturbations in a universe containing a significant population of massive neutrinos are calculated. Because linear perturbations in the neutrino density are subject to nonviscous damping on length scales smaller than the effective neutrino Jeans length, the fluctuation spectrum of the neutrino density perturbations just after photon decoupling is expected to peak near the maximum neutrino Jeans mass. The gravitational effects of nonneutrino species are included in calculating the maximum neutrino Jeans mass, which is found to be [M/sub J/(t)]/sub max/approx.10 17 M/sub sun//[m/sub ν/(eV)] 2 , about an order of magnitude smaller than is obtained when nonneutrino species are ignored. An explicit expression for the nonviscous damping of neutrino density perturbations less massive than the maximum neutrino Jeans mass is derived. The linear evolution of density perturbations after photon decoupling is discussed. Of particular interest is the possibility that fluctuations in the neutrino density induce baryon density perturbations after photon decoupling and that the maximum neutrino Jeans determines the characteristic bound mass of galaxy clusters

  5. Geometry of perturbed Gaussian states and quantum estimation

    International Nuclear Information System (INIS)

    Genoni, Marco G; Giorda, Paolo; Paris, Matteo G A

    2011-01-01

    We address the non-Gaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that the nG of the perturbed state may be written as the quantum Fisher information (QFI) distance minus a term depending on the infinitesimal energy change, i.e. it provides a lower bound to statistical distinguishability. Upon moving on isoenergetic surfaces in a neighbourhood of a Gaussian state, nG thus coincides with a proper distance in the Hilbert space and exactly quantifies the statistical distinguishability of the perturbations. On the other hand, for perturbations leaving the covariance matrix unperturbed, we show that nG provides an upper bound to the QFI. Our results show that the geometry of non-Gaussian states in the neighbourhood of a Gaussian state is definitely not trivial and cannot be subsumed by a differential structure. Nevertheless, the analysis of perturbations to a Gaussian state reveals that nG may be a resource for quantum estimation. The nG of specific families of perturbed Gaussian states is analysed in some detail with the aim of finding the maximally non-Gaussian state obtainable from a given Gaussian one. (fast track communication)

  6. Study on Scattering Theory and Perturbative Quantum Chromodynamics: case of quark-antiquark Top pair production

    International Nuclear Information System (INIS)

    Randriamisy, H.D.E.

    2014-01-01

    Nowadays, the study of scattering and production of particles occupies an important place in subatomic physics research. The main ongoing experiments concern high-energy scattering in the colliders, the scattering theory based on quantum field theory is used for the theoretical study. The work presented in this thesis is located in this framework, in fact it concerns a study on the scattering theory and Perturbative Quantum Chromodynamics. We used the path integral formalism of quantum field theory and perturbation theory. As we considered the higher order corrections in perturbative developments, the renormalization theory with the method of dimensional regularization was also used. As an application, the case of the Top quark production was considered. As main results, we can quote the obtention of the cross section of quark-antiquark top pair production up to second order. [fr

  7. New numerical method for iterative or perturbative solution of quantum field theory

    International Nuclear Information System (INIS)

    Hahn, S.C.; Guralnik, G.S.

    1999-01-01

    A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)

  8. Healthy imperfect dark matter from effective theory of mimetic cosmological perturbations

    International Nuclear Information System (INIS)

    Hirano, Shin'ichi; Nishi, Sakine; Kobayashi, Tsutomu

    2017-01-01

    We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar perturbations. To seek for an instability-free extension of imperfect dark matter, we develop an effective theory of cosmological perturbations subject to the constraint on the scalar field's kinetic term. This is done by using the unifying framework of general scalar-tensor theories based on the ADM formalism. We demonstrate that it is indeed possible to construct a model of imperfect dark matter which is free from ghost and gradient instabilities. As a side remark, we also show that mimetic F (R) theory is plagued with the Ostrogradsky instability.

  9. Healthy imperfect dark matter from effective theory of mimetic cosmological perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Hirano, Shin' ichi; Nishi, Sakine; Kobayashi, Tsutomu, E-mail: s.hirano@rikkyo.ac.jp, E-mail: sakine@rikkyo.ac.jp, E-mail: tsutomu@rikkyo.ac.jp [Department of Physics, Rikkyo University, Toshima, Tokyo 171-8501 (Japan)

    2017-07-01

    We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar perturbations. To seek for an instability-free extension of imperfect dark matter, we develop an effective theory of cosmological perturbations subject to the constraint on the scalar field's kinetic term. This is done by using the unifying framework of general scalar-tensor theories based on the ADM formalism. We demonstrate that it is indeed possible to construct a model of imperfect dark matter which is free from ghost and gradient instabilities. As a side remark, we also show that mimetic F (R) theory is plagued with the Ostrogradsky instability.

  10. Extended Møller-Plesset perturbation theory for dynamical and static correlations

    International Nuclear Information System (INIS)

    Tsuchimochi, Takashi; Van Voorhis, Troy

    2014-01-01

    We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter

  11. Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction

    Energy Technology Data Exchange (ETDEWEB)

    Pastorczak, Ewa; Prlj, Antonio; Corminboeuf, Clémence, E-mail: clemence.corminboeuf@epfl.ch [Laboratory for Computational Molecular Design, Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne (Switzerland); Gonthier, Jérôme F. [Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 (United States)

    2015-12-14

    We introduce an intramolecular energy decomposition scheme for analyzing non-covalent interactions within molecules in the spirit of symmetry-adapted perturbation theory (SAPT). The proposed intra-SAPT approach is based upon the Chemical Hamiltonian of Mayer [Int. J. Quantum Chem. 23(2), 341–363 (1983)] and the recently introduced zeroth-order wavefunction [J. F. Gonthier and C. Corminboeuf, J. Chem. Phys. 140(15), 154107 (2014)]. The scheme decomposes the interaction energy between weakly bound fragments located within the same molecule into physically meaningful components, i.e., electrostatic-exchange, induction, and dispersion. Here, we discuss the key steps of the approach and demonstrate that a single-determinant wavefunction can already deliver a detailed and insightful description of a wide range of intramolecular non-covalent phenomena such as hydrogen bonds, dihydrogen contacts, and π − π stacking interactions. Intra-SAPT is also used to shed the light on competing intra- and intermolecular interactions.

  12. Comparing energy loss and pperpendicular -broadening in perturbative QCD with strong coupling N=4 SYM theory

    International Nuclear Information System (INIS)

    Dominguez, Fabio; Marquet, C.; Mueller, A.H.; Wu Bin; Xiao, Bo-Wen

    2008-01-01

    We compare medium induced energy loss and p perpendicular -broadening in perturbative QCD with that of the trailing string picture of SYM theory. We consider finite and infinite extent matter as well as relativistic heavy quarks which correspond to those being produced in the medium or external to it. When expressed in terms of the appropriate saturation momentum, we find identical parametric forms for energy loss in perturbative QCD and SYM theory. We find simple correspondences between p perpendicular -broadening in QCD and in SYM theory although p perpendicular -broadening is radiation dominated in SYM theory and multiple scattering dominated in perturbative QCD

  13. On the loop-loop scattering amplitudes in Abelian and non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Meggiolaro, Enrico

    2005-01-01

    The high-energy elastic scattering amplitude of two colour-singlet qq-bar pairs is governed by the correlation function of two Wilson loops, which follow the classical straight lines for quark (antiquark) trajectories. This quantity is expected to be free of IR divergences, differently from what happens for the parton-parton elastic scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR finiteness by a direct non-perturbative computation of the loop-loop scattering amplitudes in the (pedagogic, but surely physically interesting) case of quenched QED. The results obtained for the Abelian case will be generalized to the case of a non-Abelian gauge theory with Nc colours, but stopping to the order O(g4) in perturbation theory. In connection with the above-mentioned IR finiteness, we shall also discuss some analytic properties of the loop-loop scattering amplitudes in both Abelian and non-Abelian gauge theories, when going from Minkowskian to Euclidean theory, which can be relevant to the still unsolved problem of the s-dependence of hadron-hadron total cross-sections

  14. T-odd correlations in radiative K+l3 decays and chiral perturbation theory

    International Nuclear Information System (INIS)

    Mueller, E.H.; Kubis, B.; Meissner, U.G.

    2006-01-01

    The charged kaon decay channel K + l3γ allows for studies of direct CP violation, possibly due to non-standard mechanisms, with the help of T-odd correlation variables. In order to be able to extract a CP-violating signal from experiment, it is necessary to understand all possible standard model phases that also produce T-odd asymmetries. We complement earlier studies by considering strong interaction phases in hadronic structure functions that appear at higher orders in chiral perturbation theory, and we compare our findings to other potential sources of asymmetries. (orig.)

  15. Dissipative motion perturbation theory and exact solutions

    International Nuclear Information System (INIS)

    Lodder, J.J.

    1976-06-01

    Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion

  16. Solving the open bosonic string in perturbation theory

    International Nuclear Information System (INIS)

    Samuel, S.

    1990-01-01

    The integrand and integration region for the N-point amplitude in the open oriented bosonic string are obtained to all orders in perturbation theory. The result is derived from the Witten covariant string field theory by using on-shell and off-shell conformal methods and Riemann surface mathematics. Although only the off-shell g-loop tachyon amplitudes are computed explicitly, the methods generalize to other external states. We derive the g-loop ghost-Jacobi identity in which the ghost correlation function cancels the jacobian factor in changing from second-quantized to first-quantized variables. Moduli space is discussed from several viewpoints and it is shown that string field theory provides an algorithm for its determination. (orig.)

  17. Introduction and overview to some topics in perturbative QCD and their relationship to non perturbative effects

    International Nuclear Information System (INIS)

    West, G.

    1990-01-01

    The main thrust of this talk is to review and discuss various topics in both perturbative and non-perturbative QCD that are, by and large, model independent. This inevitably means that we shall rely heavily on the renormalization group and asymptotic freedom. Although this usually means that one has to concentrate on high energy phenomena, there are some physical processes even involving bound states which are certainly highly non-perturbative, where one can make some progress without becoming overly model independent. Experience with the EMC effect, where there are about as many ''explanations'' as authors, has surely taught us that it may well be worth returning to ''basics'' and thinking about general properties of QCD rather than guessing, essentially arbitrarily, what we think is its low energy structure. No doubt we shall have to await further numerical progress or for some inspired theoretical insight before we can, with confidence, attack these extremely difficult problems. So, with this in mine, I shall review a smattering of problems which do have a non-perturbative component and where some rather modest progress can actually be made; I emphasize the adjective ''modest''exclamation point

  18. Estimation of high orders of the perturbation theory in quantum mechanics

    International Nuclear Information System (INIS)

    Seznec, Reynald.

    1978-01-01

    First of all the simple case of an integral of one variable (zero-dimensional model) is examined to illustrate the methods and concepts used. A system n quantum oscillators 0(n) (spherical model) is then studied. A theory of perturbations around the saddle point dominating the functional integral is developed (theory of perturbations around the instanton). The fluctuation propagator is calculated explicitly. Some properties of the corresponding Feynman diagrams are also investigated. Methods are proposed to generalize the calculations to more complicated potentials. As an example of application the calculations of the first correction to the Lipatovian term are given for the spherical model [fr

  19. Perturbative quantum field theory in the framework of the fermionic projector

    International Nuclear Information System (INIS)

    Finster, Felix

    2014-01-01

    We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur

  20. Perturbative Quantum Field Theory in the Framework of the Fermionic Projector

    OpenAIRE

    Finster, Felix

    2013-01-01

    We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

  1. Perturbative quantum field theory in the framework of the fermionic projector

    Energy Technology Data Exchange (ETDEWEB)

    Finster, Felix, E-mail: finster@ur.de [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany)

    2014-04-15

    We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

  2. Perturbative quantum field theory in the framework of the fermionic projector

    Science.gov (United States)

    Finster, Felix

    2014-04-01

    We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

  3. Adiabatic perturbation theory in quantum dynamics

    CERN Document Server

    Teufel, Stefan

    2003-01-01

    Separation of scales plays a fundamental role in the understanding of the dynamical behaviour of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. This book focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit. A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED.

  4. Perturbation theory in nuclear fuel management optimization

    International Nuclear Information System (INIS)

    Ho, L.W.; Rohach, A.F.

    1982-01-01

    Perturbation theory along with a binary fuel shuffling technique is applied to predict the effects of various core configurations and, hence, the optimization of in-core fuel management. The computer code FULMNT has been developed to shuffle the fuel assemblies in search of the lowest possible power peaking factor. An iteration approach is used in the search routine. A two-group diffusion theory method is used to obtain the power distribution for the iterations. A comparison of the results of this method with other methods shows that this approach can save computer time and obtain better power peaking factors. The code also has a burnup capability that can be used to check power peaking throughout the core life

  5. Perturbation theory for nematic liquid crystals of axially symmetric molecules: Evaluation of fourth rank orientational order parameter

    International Nuclear Information System (INIS)

    Singh, K.

    1993-11-01

    Using a statistical mechanical perturbation theory for isotropic-nematic transition we report a calculation of second and fourth rank orientation order parameters and thermodynamic properties for a model system of prolate ellipsoids of revolution parameterized by its length-to-width ratio. The influence of attractive potential represented by dispersion interaction on a variety of thermodynamic properties is analysed. Inclusion of fourth rank orientational order parameter in calculation slightly changes the transition parameter. (author). 7 refs, 1 tab

  6. The status and prospects of quantum non-local field theory

    International Nuclear Information System (INIS)

    Cornish, N.J.; Melbourne Univ., Parkville

    1991-01-01

    A critical review of the physical constraints on the form the non-locality can take is presented. The conclusion of this review is that non-locality must be restricted to interactions with the vacuum sea of virtual particles. A successful formulation of such a theory, Quantum Nonlocal Field Theory (QNFT), is applied to scalar electrodynamics and serves to illustrate how gauge invariance and manifest finiteness can be achieved. The importance of the infinite dimensional symmetry groups that occur in QNFT are discussed as an alternative to supersymmetry, the ability to generate masses by breaking the non-local symmetry with a non-invariant functional measure is given a critical assessment. To demonstrate some of the many novel applications QNFT may make possible, three disparate examples are mooted, the existence of electroweak monopoles, an mechanism for CP violation and the formulation of a finite perturbative theory of Quantum Gravity. 21 refs., ills

  7. Generalized perturbation theory in DRAGON: application to CANDU cell calculations

    International Nuclear Information System (INIS)

    Courau, T.; Marleau, G.

    2001-01-01

    Generalized perturbation theory (GPT) in neutron transport is a means to evaluate eigenvalue and reaction rate variations due to small changes in the reactor properties (macroscopic cross sections). These variations can be decomposed in two terms: a direct term corresponding to the changes in the cross section themselves and an indirect term that takes into account the perturbations in the neutron flux. As we will show, taking into account the indirect term using a GPT method is generally straight forward since this term is the scalar product of the unperturbed generalized adjoint with the product of the variation of the transport operator and the unperturbed flux. In the case where the collision probability (CP) method is used to solve the transport equation, evaluating the perturbed transport operator involves calculating the variations in the CP matrix for each change in the reactor properties. Because most of the computational effort is dedicated to the CP matrix calculation the gains expected form the GPT method would therefore be annihilated. Here we will present a technique to approximate the variations in the CP matrices thereby replacing the variations in the transport operator with source term variations. We will show that this approximation yields errors fully compatible with the standard generalized perturbation theory errors. Results for 2D CANDU cell calculations will be presented. (author)

  8. Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory(FSDT) and perturbation method

    Science.gov (United States)

    Khoshgoftar, M. J.; Mirzaali, M. J.; Rahimi, G. H.

    2015-11-01

    Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

  9. FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Fang, Xiao; Blazek, Jonathan A.; McEwen, Joseph E.; Hirata, Christopher M., E-mail: fang.307@osu.edu, E-mail: blazek@berkeley.edu, E-mail: mcewen.24@osu.edu, E-mail: hirata.10@osu.edu [Center for Cosmology and AstroParticle Physics, Department of Physics, The Ohio State University, 191 W Woodruff Ave, Columbus OH 43210 (United States)

    2017-02-01

    Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.

  10. Strong/weak coupling duality relations for non-supersymmetric string theories

    International Nuclear Information System (INIS)

    Blum, J.D.; Dienes, K.R.

    1998-01-01

    Both the supersymmetric SO(32) and E 8 x E 8 heterotic strings in ten dimensions have known strong-coupling duals. However, it has not been known whether there also exist strong-coupling duals for the non-supersymmetric heterotic strings in ten dimensions. In this paper, we construct explicit open-string duals for the circle compactifications of several of these non-supersymmetric theories, among them the tachyon-free SO(16) x SO(16) string. Our method involves the construction of heterotic and open-string interpolating models that continuously connect non-supersymmetric strings to supersymmetric strings. We find that our non-supersymmetric dual theories have exactly the same massless spectra as their heterotic counterparts within a certain range of our interpolations. We also develop a novel method for analyzing the solitons of non-supersymmetric open-string theories, and find that the solitons of our dual theories also agree with their heterotic counterparts. These are therefore the first known examples of strong/weak coupling duality relations between non-supersymmetric, tachyon-free string theories. Finally, the existence of these strong-coupling duals allows us to examine the non-perturbative stability of these strings, and we propose a phase diagram for the behavior of these strings as a function of coupling and radius. (orig.)

  11. O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory

    CERN Document Server

    Grimbach, A; Knechtli, F; Palombi, Filippo

    2008-01-01

    We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schroedinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart.

  12. Statistical theory of signal detection

    CERN Document Server

    Helstrom, Carl Wilhelm; Costrell, L; Kandiah, K

    1968-01-01

    Statistical Theory of Signal Detection, Second Edition provides an elementary introduction to the theory of statistical testing of hypotheses that is related to the detection of signals in radar and communications technology. This book presents a comprehensive survey of digital communication systems. Organized into 11 chapters, this edition begins with an overview of the theory of signal detection and the typical detection problem. This text then examines the goals of the detection system, which are defined through an analogy with the testing of statistical hypotheses. Other chapters consider

  13. A global numerical solution of the radial Schroedinger equation by second-order perturbation theory

    International Nuclear Information System (INIS)

    Adam, G.

    1979-01-01

    A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)

  14. Analytic perturbation theory in analyzing some QCD observables

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    2001-01-01

    The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD - ghost singularities and with the resume of this trouble solution within the APT. By a few examples in the various energy and momentum transfer regions (with the flavor number f = 3, 4 and 5) we demonstrate the effect of improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution (of an order of α s 3 ) is as a rule numerically inessential. This raises hope for practical solving the well-known problem of asymptotic nature of common QFT perturbation series. The second conclusion is that a common perturbative analysis of time-like events with the big π 2 term in the π 2 coefficient is not adequate at s ≤ 2 GeV 2 . In particular, this relates to τ decay. Then, for the 'high' (f = 5) region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at 10 GeV ≤ √s ≤ 170 GeV) for analysis of shape/events data contains a systematic negative error of a 1 - 2 per cent level for the extracted α bar s (2) values. Our physical conclusion is that the α bar s (M Z 2 ) value averaged over the f = 5 data s (M Z 2 )> APT; f= 5 ≅ 0.124 appreciably differs from the currently accepted 'world average' (= 0.118)

  15. Introduction to non-perturbative quantum chromodynamics

    International Nuclear Information System (INIS)

    Pene, O.

    1995-01-01

    Quantum chromodynamics is considered to be the theory of strong interaction. The main peculiarity of this theory is that its asymptotic states (hadrons) are different from its elementary fields (quarks and gluons). This property plays a great part in any physical process involving small momentum-energy transfers. In such a range perturbative methods are no longer allowed. This work focuses on other tools such as QCD symmetry, the quark model, Green functions and the sum rules. To get hadron characteristics numerically, QCD on lattices is used but only in the case of simple process involving no more than one hadron in the initial and final states because of the complexity of the Green function. Some examples using a Monte-Carlo simulation are given. (A.C.)

  16. Meson-baryon scattering in manifestly Lorentz invariant chiral perturbation theory

    International Nuclear Information System (INIS)

    Mai, Maxim; Bruns, Peter C.; Kubis, Bastian; Meissner, Ulf-G.

    2011-01-01

    We analyze meson-baryon scattering lengths in the framework of covariant baryon chiral perturbation theory at leading one-loop order. We compute the complete set of matching relations between the dimension-two low-energy constants in the two- and three-flavor formulations of the theory. We derive new two-flavor low-energy theorems for pion-hyperon scattering that can be tested in lattice simulations.

  17. Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory

    International Nuclear Information System (INIS)

    Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki

    2009-01-01

    Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to 'pion' fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

  18. Cosmological perturbations in non-local higher-derivative gravity

    International Nuclear Information System (INIS)

    Craps, Ben; Jonckheere, Tim De; Koshelev, Alexey S.

    2014-01-01

    We study cosmological perturbations in a non-local higher-derivative model of gravity introduced by Biswas, Mazumdar and Siegel. We extend previous work, which had focused on classical scalar perturbations around a cosine hyperbolic bounce solution, in three ways. First, we point out the existence of a Starobinsky solution in this model, which is more attractive from a phenomenological point of view (even though it has no bounce). Second, we study classical vector and tensor pertuxsxrbations. Third, we show how to quantize scalar and tensor perturbations in a de Sitter phase (for choices of parameters such that the model is ghost-free). Our results show that the model is well-behaved at this level, and are very similar to corresponding results in local f(R) models. In particular, for the Starobinsky solution of non-local higher-derivative gravity, we find the same tensor-to-scalar ratio as for the conventional Starobinsky model

  19. Statistical theory and inference

    CERN Document Server

    Olive, David J

    2014-01-01

    This text is for  a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful  tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.

  20. Perturbation approach to the self-energy of non-S hydrogenic states

    International Nuclear Information System (INIS)

    Le Bigot, Eric-Olivier; Jentschura, Ulrich D.; Mohr, Peter J.; Indelicato, Paul; Soff, Gerhard

    2003-01-01

    We present results on the self-energy correction to the energy levels of hydrogen and hydrogenlike ions. The self-energy represents the largest QED correction to the relativistic (Dirac-Coulomb) energy of a bound electron. We focus on the perturbation expansion of the self-energy of non-S states, and provide estimates of the so-called A 60 perturbation coefficient, which can be viewed as a relativistic Bethe logarithm. Precise values of A 60 are given for many P, D, F, and G states, while estimates are given for other states. These results can be used in high-precision spectroscopy experiments in hydrogen and hydrogenlike ions. They yield the best available estimate of the self-energy correction of many atomic states

  1. Perturbative evaluation of the Thermal Wilson Loop

    International Nuclear Information System (INIS)

    Gava, E.; Jengo, R.

    1981-06-01

    The Thermal Wilson Loop 0 sup(β) dtauA 0 (tau, x-vector)>, representing an order parameter for the gauge theory and expected to be zero in the confining phase, is perturbatively evaluated up to the O(g 4 ) included for an SU(N) pure Yang-Mills theory. This evaluation should be meaningful at high temperature, β → 0. Its behaviour is discussed and a possible need for non-perturbative instanton-like contributions is pointed out. (author)

  2. The method of rigged spaces in singular perturbation theory of self-adjoint operators

    CERN Document Server

    Koshmanenko, Volodymyr; Koshmanenko, Nataliia

    2016-01-01

    This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...

  3. Semiclassical perturbation theory for diffraction in heavy atom surface scattering.

    Science.gov (United States)

    Miret-Artés, Salvador; Daon, Shauli; Pollak, Eli

    2012-05-28

    The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.

  4. Renormalization of quantum electrodynamics in an arbitrarily strong time independent external field. [Perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Dosch, H G [Heidelberg Univ. (F.R. Germany). Inst. fuer Theoretische Physik; Mueller, V F [Trier-Kaiserslautern Univ., Kaiserslautern (F.R. Germany). Fachbereich Physik

    1975-01-01

    Extending the inductive renormalization procedure of Epstein and Glaser which is essentially based on locality, we show that quantum electrodynamics in an external time independent electromagnetic field has a renormalizable formal perturbation expansion. The interaction involving the quantized radiation field but not the action of the external field is treated by perturbation theory. It turns out that vacuum polarization is undetermined in the framework of such a theory.

  5. Perturbation theory for the effective diffusion constant in a medium of random scatterers

    International Nuclear Information System (INIS)

    Dean, D S; Drummond, I T; Horgan, R R; Lefevre, A

    2004-01-01

    We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random medium. The random medium contains point scatterers of density ρ uniformly distributed throughout the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis, we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalization group approach based on thinning out the scatterers; this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme, its predictions are confronted with results obtained by numerical simulation

  6. Asymptotic propagators and trajectories in plasma turbulence theory. The importance of irreversibility, asymptoticity and non-Markovian terms

    International Nuclear Information System (INIS)

    Misguich, J.H.

    1978-09-01

    The physical meaning of perturbed trajectories in turbulent fields is analysed. Special care is devoted to the asymptotic description of average trajectories for long time intervals, as occuring in many recent plasma turbulence theories. Equivalence is proved between asymptotic average trajectories described as well (i) by the propagators V(t,t-tau) for retrodiction and Wsub(J)(t,t+tau) for prediction, and (ii) by the long time secular behavior of the solution of the equations of motion. This confirms the equivalence between perturbed orbit theories and renormalized theories, including non-Markovian contributions

  7. S-duality invariant perturbation theory improved by holography

    Energy Technology Data Exchange (ETDEWEB)

    Chowdhury, Abhishek [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); Honda, Masazumi [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 7610001 (Israel); Thakur, Somyadip [Tata Institute of Fundamental Research,Mumbai 400005 (India)

    2017-04-26

    We study anomalous dimensions of unprotected low twist operators in the four-dimensional SU (N)N=4 supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling τ. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test a recent conjecture by the N=4 superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points τ=i and τ=e{sup iπ/3}. It turns out that our interpolating functions have maximum at τ=e{sup iπ/3}, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw the image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We also construct interpolating functions for the subleading twist operator and study level crossing phenomenon between the leading and subleading twist operators. Finally we study the dimension of the Konishi operator in the planar limit. We find that our interpolating functions match with numerical result obtained by Thermodynamic Bethe Ansatz very well. It turns out that analytic properties of the interpolating functions reflect an expectation on a radius of convergence of the perturbation theory.

  8. Quantum field theory with a momentum space of constant curvature (perturbation theory)

    International Nuclear Information System (INIS)

    Mir-Kasimov, R.M.

    1978-01-01

    In the framework of the field-theoretical approach in which the off-the-mass shell extension proceeds in the p-space of constant curvature, the perburbation theory is developed. The configurational representation of the de Sitter space is introduced with the help of the Fourier transformation of the group of motions. On the basis of a natural generalization of the Bogolyubov causality condition to the case of the new configurational representation a perturbation theory is constructed with the local in xi space Lagrangian density fucntion. The obtained S matrix obeys the reguirement of translation invariance. The S matrix elements are given by convergent expressions

  9. Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations

    Science.gov (United States)

    Gidea, Marian; de la Llave, Rafael

    2018-04-01

    We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold Λ _0 . We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ɛ \\in R . For all |ɛ | sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold \\tilde{Λ }_ɛ . For ɛ =0 , \\tilde{Λ }_0=Λ _0× R . We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of \\tilde{Λ }_0 under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of \\tilde{Λ }_ɛ , W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) , respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order O(ɛ ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in Λ _0 , and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on

  10. Continuum regularized Yang-Mills theory

    International Nuclear Information System (INIS)

    Sadun, L.A.

    1987-01-01

    Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

  11. Constructive renormalization theory

    International Nuclear Information System (INIS)

    Rivasseau, Vincent

    2000-01-01

    These notes are the second part of a common course on Renormalization Theory given with Professor P. da Veiga. I emphasize here the rigorous non-perturbative or constructive aspects of the theory. The usual formalism for the renormalization group in field theory or statistical mechanics is reviewed, together with its limits. The constructive formalism is introduced step by step. Taylor forest formulas allow to perform easily the cluster and Mayer expansions which are needed for a single step of the renormalization group in the case of Bosonic theories. The iteration of this single step leads to further difficulties whose solution is briefly sketched. The second part of the course is devoted to Fermionic models. These models are easier to treat on the constructive level so they are very well suited to beginners in constructive theory. It is shown how the Taylor forest formulas allow to reorganize perturbation theory nicely in order to construct the Gross-Neveu 2 model without any need for cluster or Mayer expansions. Finally applications of this technique to condensed matter and renormalization group around Fermi surface are briefly reviewed. (author)

  12. Illustrated study of the semi-holographic non-perturbative framework

    NARCIS (Netherlands)

    Banerjee, Souvik; Gaddam, Nava; Mukhopadhyay, Ayan

    2017-01-01

    Semi-holography has been proposed as an effective nonperturbative framework which can combine perturbative and nonperturbative effects consistently for theories like QCD. It is postulated that the strongly coupled nonperturbative sector has a holographic dual in the form of a classical gravity

  13. On the all-order perturbative finiteness of the deformed N=4 SYM theory

    International Nuclear Information System (INIS)

    Rossi, G.C.; Sokatchev, E.; Stanev, Ya.S.

    2006-01-01

    We prove that the chiral propagator of the deformed N=4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g. We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g 6

  14. Disformal transformation of cosmological perturbations

    International Nuclear Information System (INIS)

    Minamitsuji, Masato

    2014-01-01

    We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame

  15. Dynamical affine symmetry and covariant perturbation theory for gravity

    International Nuclear Information System (INIS)

    Pervushin, V.N.

    1975-01-01

    The covariant perturbation theory for gravity with the simplest reduction properties is formulated. The main points are as follows: fundamental fields are the normal coordinates of ten-dimensional space of the gravitational field, and the fields are separated into the classical (background) and quantum ones in the generating functional along geodesics of this space

  16. Foundations of quantum chromodynamics: Perturbative methods in gauge theories

    International Nuclear Information System (INIS)

    Muta, T.

    1986-01-01

    This volume develops the techniques of perturbative QCD in great detail starting with field theory. Aside from extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions, this book provides a comprehensive introduction to gauge field theories. Examples and exercises are provided to amplify the discussions on important topics. Contents: Introduction; Elements of Quantum Chromodynamics; The Renormalization Group Method; Asymptotic Freedom; Operator Product Expansion Formalism; Applications; Renormalization Scheme Dependence; Factorization Theorem; Further Applications; Power Corrections; Infrared Problem. Power Correlations; Infrared Problem

  17. Perturbative search for dead-end CFTs

    International Nuclear Information System (INIS)

    Nakayama, Yu

    2015-01-01

    To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a. dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as O(10"−"5) and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.

  18. Baryon chiral perturbation theory extended beyond the low-energy region.

    Science.gov (United States)

    Epelbaum, E; Gegelia, J; Meißner, Ulf-G; Yao, De-Liang

    We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is, we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants, which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.

  19. Multidimensional periodic Schrödinger operator perturbation theory and applications

    CERN Document Server

    Veliev, Oktay

    2015-01-01

    The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the ...

  20. Baryon chiral perturbation theory extended beyond the low-energy region

    International Nuclear Information System (INIS)

    Epelbaum, E.; Gegelia, J.; Meissner, Ulf G.; Yao, De-Liang

    2015-01-01

    We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is, we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants, which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region. (orig.)

  1. Green's functions for theories with massless particles (in perturbation theory). [Growth properties, momentum space, mass renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Blanchard, P [European Organization for Nuclear Research, Geneva (Switzerland); Seneor, R [European Organization for Nuclear Research, Geneva (Switzerland); Ecole Polytechnique, 75 - Paris (France). Centre de Physique Theorique)

    1975-01-01

    With the method of perturbative renormalization developed by Epstein and Glaser it is shown that Green's functions exist for theories with massless particles such as Q.E.D. and lambda:PHI/sup 2n/ theories. Growth properties are given in momentum space. In the case of Q.E.D., it is also shown that one can perform the physical mass renormalization.

  2. Non-Vacuum Initial States for Cosmological Perturbations of Quantum-Mechanical Origin

    CERN Document Server

    Martín, J; Sakellariadou, M; Martin, Jerome; Riazuelo, Alain; Sakellariadou, Mairi

    2000-01-01

    In the context of inflation, non-vacuum initial states for cosmological perturbations that possess a built in scale are studied. It is demonstrated that this assumption leads to a falsifiable class of models. The question of whether they lead to conflicts with the available observations is addressed. For this purpose, the power spectrum of the Bardeen potential operator is calculated and compared with the CMBR anisotropies measurements and the redshift surveys of galaxies and clusters of galaxies. Generic predictions of the model are: a high first acoustic peak, the presence of a bump in the matter power spectrum and non-Gaussian statistics. The details are controlled by the number of quanta in the non-vacuum initial state. Comparisons with observations show that there exists a window for the free parameters such that good agreement between the data and the theoretical predictions is possible. However, in the case where the initial state is a state with a fixed number of quanta, it is shown that this number c...

  3. Fundamental frequency and voice perturbation measures in smokers and non-smokers: An acoustic and perceptual study

    Science.gov (United States)

    Freeman, Allison

    This research examined the fundamental frequency and perturbation (jitter % and shimmer %) measures in young adult (20-30 year-old) and middle-aged adult (40-55 year-old) smokers and non-smokers; there were 36 smokers and 36 non-smokers. Acoustic analysis was carried out utilizing one task: production of sustained /a/. These voice samples were analyzed utilizing Multi-Dimensional Voice Program (MDVP) software, which provided values for fundamental frequency, jitter %, and shimmer %.These values were analyzed for trends regarding smoking status, age, and gender. Statistical significance was found regarding the fundamental frequency, jitter %, and shimmer % for smokers as compared to non-smokers; smokers were found to have significantly lower fundamental frequency values, and significantly higher jitter % and shimmer % values. Statistical significance was not found regarding fundamental frequency, jitter %, and shimmer % for age group comparisons. With regard to gender, statistical significance was found regarding fundamental frequency; females were found to have statistically higher fundamental frequencies as compared to males. However, the relationships between gender and jitter % and shimmer % lacked statistical significance. These results indicate that smoking negatively affects voice quality. This study also examined the ability of untrained listeners to identify smokers and non-smokers based on their voices. Results of this voice perception task suggest that listeners are not accurately able to identify smokers and non-smokers, as statistical significance was not reached. However, despite a lack of significance, trends in data suggest that listeners are able to utilize voice quality to identify smokers and non-smokers.

  4. Use of the Halbach perturbation theory for the multipole design of the ALS storage ring sextupole

    Energy Technology Data Exchange (ETDEWEB)

    Marks, S. [Lawrence Berkeley Lab., CA (United States)

    1995-02-01

    The Advanced Light Source (ALS) storage ring sextupole is a unique multi-purpose magnet. It is designed to operate in the primary or sextupole mode and in three auxiliary trim modes: horizontal steering, vertical steering, and skew quadrupole. Klaus Halbach developed a perturbation theory for iron-dominated magnets which provides the basis for this design. Many magnet designers, certainly those who have been exposed to Klaus, are familiar with this theory and have used it for such things as evaluating the effect of assembly alignment errors. The ALS sextupole design process was somewhat novel in its use of the perturbation theory to design essential features of the magnet. In particular, the steering and skew quadrupole functions are produced by violating sextupole symmetry and are thus perturbations of the normal sextupole excitation. The magnet was designed such that all four modes are decoupled and can be excited independently. This paper discusses the use of Halbach`s perturbation theory to design the trim functions and to evaluate the primary asymmetry in the sextupole mode, namely, a gap in the return yoke to accommodate the vacuum chamber. Prototype testing verified all operating modes of the magnet and confirmed the expected performance from calculations based upon the Halbach perturbation theory. A total of 48 sextupole magnets of this design are now installed and operating successfully in the ALS storage ring.

  5. GAPER-1D, 1-D Multigroup 1. Order Perturbation Transport Theory for Reactivity Coefficient

    International Nuclear Information System (INIS)

    Koch, P.K.

    1976-01-01

    1 - Description of problem or function: Reactivity coefficients are computed using first-order transport perturbation theory for one- dimensional multi-region reactor assemblies. The number of spatial mesh-points and energy groups is arbitrary. An elementary synthesis scheme is employed for treatment of two- and three-dimensional problems. The contributions to the change in inverse multiplication factor, delta(1/k), from perturbations in the individual capture, net fission, total scattering, (n,2n), inelastic scattering, and leakage cross sections are computed. A multi-dimensional prompt neutron lifetime calculation is also available. 2 - Method of solution: Broad group cross sections for the core and perturbing or sample materials are required as input. Scalar neutron fluxes and currents, as computed by SN transport calculations, are then utilized to solve the first-order transport perturbation theory equations. A synthesis scheme is used, along with independent SN calculations in two or three dimensions, to treat a multi- dimensional assembly. Spherical harmonics expansions of the angular fluxes and scattering source terms are used with leakage and anisotropic scattering treated in a P1 approximation. The angular integrations in the perturbation theory equations are performed analytically. Various reactivity coefficients and material worths are then easily computed at specified positions in the assembly. 3 - Restrictions on the complexity of the problem: The formulation of the synthesis scheme used for two- and three-dimensional problems assumes that the fluxes and currents were computed by the DTF4 code (NESC Abstract 209). Therefore, fluxes and currents from two- or three-dimensional transport or diffusion theory codes cannot be used

  6. Loschmidt echo for local perturbations: non-monotonic cross-over from the Fermi-golden-rule to the escape-rate regime

    International Nuclear Information System (INIS)

    Goussev, Arseni; Waltner, Daniel; Richter, Klaus; Jalabert, Rodolfo A

    2008-01-01

    We address the sensitivity of quantum mechanical time evolution by considering the time decay of the Loschmidt echo (LE) (or fidelity) for local perturbations of the Hamiltonian. Within a semiclassical approach, we derive analytical expressions for the LE decay for chaotic systems for the whole range from weak to strong local perturbations and identify different decay regimes which complement those known for the case of global perturbations. For weak perturbations, a Fermi-golden-rule (FGR)-type behavior is recovered. For strong perturbations, the escape-rate regime is reached, where the LE decays exponentially with a rate independent of the perturbation strength. The transition between the FGR regime and the escape-rate regime is non-monotonic, i.e. the rate of the exponential time-decay of the LE oscillates as a function of the perturbation strength. We further perform extensive quantum mechanical calculations of the LE based on numerical wave packet evolution, which strongly support our semiclassical theory. Finally, we discuss in some detail possible experimental realizations for observing the predicted behavior of the LE

  7. Statistical theory of heat

    CERN Document Server

    Scheck, Florian

    2016-01-01

    Scheck’s textbook starts with a concise introduction to classical thermodynamics, including geometrical aspects. Then a short introduction to probabilities and statistics lays the basis for the statistical interpretation of thermodynamics. Phase transitions, discrete models and the stability of matter are explained in great detail. Thermodynamics has a special role in theoretical physics. Due to the general approach of thermodynamics the field has a bridging function between several areas like the theory of condensed matter, elementary particle physics, astrophysics and cosmology. The classical thermodynamics describes predominantly averaged properties of matter, reaching from few particle systems and state of matter to stellar objects. Statistical Thermodynamics covers the same fields, but explores them in greater depth and unifies classical statistical mechanics with quantum theory of multiple particle systems. The content is presented as two tracks: the fast track for master students, providing the essen...

  8. Finite volume at two-loops in chiral perturbation theory

    International Nuclear Information System (INIS)

    Bijnens, Johan; Rössler, Thomas

    2015-01-01

    We calculate the finite volume corrections to meson masses and decay constants in two and three flavour Chiral Perturbation Theory to two-loop order. The analytical results are compared with the existing result for the pion mass in two-flavour ChPT and the partial results for the other quantities. We present numerical results for all quantities.

  9. Renormalization and scaling behaviour of eikonal perturbation theories. [Eikonal approximation

    Energy Technology Data Exchange (ETDEWEB)

    Din, A M [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Teoretisk Fysik; Nielsen, N K [Aarhus Univ. (Denmark)

    1975-01-04

    Some observations on the renormalization and scaling behaviour of the charged-particle propagator in scalar quantum electrodynamics, in the ordinary eikonal approximation as well as in the eikonal perturbation theory, are reported. The conclusions indicate that scaling behaviour is not realized in the simple sense.

  10. Improved Fluid Perturbation Theory: Equation of state for Fluid Xenon

    OpenAIRE

    Li, Qiong; Liu, Hai-Feng; Zhang, Gong-Mu; Zhao, Yan-Hong; Tian, Ming-Feng; Song, Hai-Feng

    2016-01-01

    The traditional fluid perturbation theory is improved by taking electronic excitations and ionizations into account, in the framework of average ion spheres. It is applied to calculate the equation of state for fluid Xenon, which turns out in good agreement with the available shock data.

  11. Critical behaviors of gravity under quantum perturbations

    Directory of Open Access Journals (Sweden)

    ZHANG Hongsheng

    2014-02-01

    Full Text Available Phase transition and critical phenomenon is a very interesting topic in thermodynamics and statistical mechanics. Gravity is believed to have deep and inherent relation to thermodynamics. Near the critical point,the perturbation becomes significant. Thus for ordinary matter (governed by interactions besides gravity the critical behavior will become very different if we ignore the perturbations around the critical point,such as mean field theory. We find that the critical exponents for RN-AdS spacetime keep the same values even when we consider the full quantum perturbations. This indicates a key difference between gravity and ordinary thermodynamic system.

  12. Nonlocal String Theories on AdS3 x S3 and Stable Non-Supersymmetric Backgrounds

    International Nuclear Information System (INIS)

    Silverstein, Eva M

    2002-01-01

    We exhibit a simple class of exactly marginal ''double-trace'' deformations of two dimensional CFTs which have AdS 3 duals, in which the deformation is given by a product of left and right-moving U(1) currents. In this special case the deformation on AdS 3 is generated by a local boundary term in three dimensions, which changes the physics also in the bulk via bulk-boundary propagators. However, the deformation is non-local in six dimensions and on the string worldsheet, like generic non-local string theories (NLSTs). Due to the simplicity of the deformation we can explicitly make computations in the non-local string theory and compare them to CFT computations, and we obtain precise agreement. We discuss the effect of the deformation on closed strings and on D-branes. The examples we analyze include a supersymmetry-breaking but exactly marginal ''double-trace'' deformation, which is dual to a string theory in which no destabilizing tadpoles are generated for moduli nonperturbatively in all couplings, despite the absence of supersymmetry. We explain how this cancellation works on the gravity side in string perturbation theory, and also non-perturbatively at leading order in the deformation parameter. We also discuss possible flat space limits of our construction

  13. Non-Perturbative Formulation of Time-Dependent String Solutions

    CERN Document Server

    Alexandre, J; Mavromatos, Nikolaos E; Alexandre, Jean; Ellis, John; Mavromatos, Nikolaos E.

    2006-01-01

    We formulate here a new world-sheet renormalization-group technique for the bosonic string, which is non-perturbative in the Regge slope alpha' and based on a functional method for controlling the quantum fluctuations, whose magnitudes are scaled by the value of alpha'. Using this technique we exhibit, in addition to the well-known linear-dilaton cosmology, a new, non-perturbative time-dependent background solution. Using the reparametrization invariance of the string S-matrix, we demonstrate that this solution is conformally invariant to alpha', and we give a heuristic inductive argument that conformal invariance can be maintained to all orders in alpha'. This new time-dependent string solution may be applicable to primordial cosmology or to the exit from linear-dilaton cosmology at large times.

  14. In-core fuel management via perturbation theory

    International Nuclear Information System (INIS)

    Mingle, J.O.

    1975-01-01

    A two-step procedure is developed for the optimization of in-core nuclear fuel management using perturbation theory to predict the effects of various core configurations. The first procedure is a cycle cost minimization using linear programming with a zoned core and discrete burnup groups. The second program utilizes an individual fuel assembly shuffling sequence to minimize the maldistribution of power generation. This latter quantity is represented by a figure of merit or by an assembly power peaking factor. A pressurized water reactor example calculation is utilized. 24 references

  15. Self-consistent many-body perturbation theory in range-separated density-functional theory

    DEFF Research Database (Denmark)

    Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard

    2008-01-01

    effects adequately which, on the other hand, can be described by many-body perturbation theory MBPT. It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short...

  16. Modified perturbation theory for strongly correlated electron systems

    International Nuclear Information System (INIS)

    Takagi, Osamu; Saso, Tetsuro

    1999-01-01

    We propose a modified scheme for calculating the single-particle excitation spectrum of the impurity Anderson model. It is based on the second order perturbation theory, but modifies the self-energy so as to reproduce the correct atomic limit and to fulfill the Friedel sum rule. Therefore, it offers a simple scheme valid over wide range of excitation energy and parameters, and would be useful also for potential application to the lattice problems. (author)

  17. Divergent Perturbation Series

    International Nuclear Information System (INIS)

    Suslov, I.M.

    2005-01-01

    Various perturbation series are factorially divergent. The behavior of their high-order terms can be determined by Lipatov's method, which involves the use of instanton configurations of appropriate functional integrals. When the Lipatov asymptotic form is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series, which can be resummed to solve various strong-coupling problems in a certain approximation. This approach is demonstrated by determining the Gell-Mann-Low functions in φ 4 theory, QED, and QCD with arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic form are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described both for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. Higher order corrections to the Lipatov asymptotic form are discussed

  18. Effective Lagrangians for SUSY QCD with properties seen in perturbation theory

    International Nuclear Information System (INIS)

    Sharatchandra, H.S.

    1984-06-01

    We construct effective Lagrangians for supersymmetric QCD which properly incorporate the relevant Ward identities and possess features encountered in perturbation theory. This shows that the unusual scenarios, proposed for SUSY QCD, are not necessary. (author)

  19. Sensitivity calculations of integral parameters by a generalyzed perturbation theory

    International Nuclear Information System (INIS)

    Santo, A.C.F. de.

    1981-12-01

    In this work, we first revise some concepts, concerning the neutron transport in nuclear systems. We derive the balance and importance equation. Then we discuss the neutron importance in subcritical, critical and supercritical systems. The adjoint flux is estabilished as the neutron importance for the fission process. The conventional perturbation theory is later presented. We developed a sistematic perturbative formulation in the first order variation in the distribution functions calculate the reactivity due to a system perturbation. We present in detail the flux difference and generalized functions methos. The above formulation is then extended for altered systems. We consider integral parameters of the type ratio of bilinear functionals (for which the reactivity is a particular case). We define sensitivity coeficients, for any integral parameter, corresponding to a especific system alterations. Possible aplication of the method are also discussed. In the last part of this work, we apply the perturbative formulation to the doppler reacitivity sensibility calculation, utilizing the generalized functions method. We describe in detail the compiler program written for this and some other possible aplications. (Author) [pt

  20. An Elementary Introduction to Statistical Learning Theory

    CERN Document Server

    Kulkarni, Sanjeev

    2011-01-01

    A thought-provoking look at statistical learning theory and its role in understanding human learning and inductive reasoning A joint endeavor from leading researchers in the fields of philosophy and electrical engineering, An Elementary Introduction to Statistical Learning Theory is a comprehensive and accessible primer on the rapidly evolving fields of statistical pattern recognition and statistical learning theory. Explaining these areas at a level and in a way that is not often found in other books on the topic, the authors present the basic theory behind contemporary machine learning and