A comprehensive coordinate space renormalization of quantum electrodynamics to two-loop order

International Nuclear Information System (INIS)

Haagensen, P.E.; Latorre, J.I.

1993-01-01

We develop a coordinate space renormalization of massless quantum electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all one- and two-loop 1PI diagrams, run renormalization group equations on them. and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle γ 5 problems

Renormalization of the inflationary perturbations revisited

Science.gov (United States)

Markkanen, Tommi

2018-05-01

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

Universal conditions for finite renormalizable quantum field theories

International Nuclear Information System (INIS)

Kranner, G.

1990-10-01

Analyzing general renormalization constants in covariant gauge and minimal subtraction, we consider universal conditions for cancelling UV-divergences in renormalizable field theories with simple gauge groups, and give constructive methods for finding nonsupersymmetric finite models. The divergent parts of the renormalization constants for fields explicitly depend on the gauge parameter ξ. Finite theories simply need finite couplings. We show that respective FinitenessConditions imply a hierarchy, the center of which are the FCs for the gauge coupling g and the Yukawa couplings of the massless theory. To gain more information about F we analyze the Yukawa-FC in greater detail. Doing so algebraically, we find out and fix all inner symmetries. Additionally, Yuakawa-couplings must be invariant under gauge transformation. Then it becomes extremely difficult to obey a FC, yield rational numbers for F ∼ 1, and satisfy the factorization-condition, unless F = 1. The particular structure of the F = 1-system allows for a most general ansatz. We figure out the simplest case, getting precisely just couplings and particle content of a general N=1-supersymmetric theory. We list a class of roughly 4000 types of theories, containing all supersymmetric, completely finite, and many more finite theories as well. (Author, shortened by Quittner) 11 figs., 54 refs

Renormalization in few body nuclear physics

Energy Technology Data Exchange (ETDEWEB)

Tomio, L.; Biswas, R. [Instituto de Fisica Teorica, UNESP, 01405-900 Sao Paulo (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminenese, Niteroi (Brazil); Frederico, T. [Instituto Tecnologico de Aeronautica, CTA 12228-900 Sao Jose dos Campos (Brazil)

2001-09-01

Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the {sup 3}S{sub l} -{sup 3} D{sub 1} states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three

Renormalization in few body nuclear physics

International Nuclear Information System (INIS)

Tomio, L.; Biswas, R.; Delfino, A.; Frederico, T.

2001-01-01

Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the 3 S l - 3 D 1 states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three-body halo nuclei is also

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)

Renormalization and effective actions for general relativity

International Nuclear Information System (INIS)

Neugebohrn, F.

2007-05-01

Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)

Renormalization and effective actions for general relativity

Energy Technology Data Exchange (ETDEWEB)

Neugebohrn, F.

2007-05-15

Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)

Renormalization of the new trajectory in the unitarized conventional dual model

International Nuclear Information System (INIS)

Quiros, M.

1978-08-01

The contribution of one-loop planar diagrams to the two-reggeon two-particle amplitude is derived. Its regge limit splits into two separate contributions which must be interpreted as renormalization effects, to order g 2 , of the α and β trajectories. It is shown that the Neveu-Scherk renormalization prescription is able to render finite both contributions. The intercept of the β trajectory is shifted from its bare value by the renormalization procedure, whereas that of the α trajectrory is not renormalized as it was required by the gauge invariance of dual theories

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

Renormalized trajectory for non-linear sigma model and improved scaling behaviour

International Nuclear Information System (INIS)

Guha, A.; Okawa, M.; Zuber, J.B.

1984-01-01

We apply the block-spin renormalization group method to the O(N) Heisenberg spin model. Extending a previous work of Hirsch and Shenker, we find the renormalized trajectory for O(infinite) in two dimensions. Four finite N models, we choose a four-parameter action near the large-N renormalized trajectory and demonstrate a remarkable improvement in the approach to continuum limit by performing Monte Carlo simulation of O(3) and O(4) models. (orig.)

Nonperturbative Renormalization of Composite Operators with Overlap Fermions

Energy Technology Data Exchange (ETDEWEB)

J.B. Zhang; N. Mathur; S.J. Dong; T. Draper; I. Horvath; F. X. Lee; D.B. Leinweber; K.F. Liu; A.G. Williams

2005-12-01

We compute non-perturbatively the renormalization constants of composite operators on a quenched 16{sup 3} x 28 lattice with lattice spacing a = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A} = Z{sub V} and Z{sub S} = Z{sub P} and find that they agree well (less than 1%) above {mu} = 1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the {ovr MS} scheme. The wave-function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

Renormalization of the QEMD of a dyon field

International Nuclear Information System (INIS)

Panagiotakopoulos, C.

1983-01-01

A renormalized quantum electromagnetodynamics (QEMD) of a dyon field is defined. Finite and n-independent answers can be obtained in each order of the loop expansion for all processes. The electric and magnetic charges are not constrained with the Dirac condition and therefore perturbation theory can be made reliable. The renormalized theory is found to possess exact dual invariance. Comparisons with the general QEMD of electric and magnetic charges are made. (orig.)

Renormalization of the QEMD of a dyon field

International Nuclear Information System (INIS)

Panagiotakopoulos, C.

1982-05-01

A renormalized quantum electromagnetodynamics (QEMD) of a dyon field is defined. Finite and n independent answers can be obtained in each order of the loop expansion for all processes. The electric and magnetic charges are not constrained with the Dirac condition and therefore perturbation theory can be made reliable. The renormalized theory is found to possess exact dual invariance. Comparisons with the general QEMD of electric and magnetic charges are made. (author)

On the renormalization of string functionals

International Nuclear Information System (INIS)

Dietz, K.; Filk, T.

1982-09-01

We investigate analytic renormalization procedures for functional integrals, corresponding to field theories defined on compact manifolds, which arise e.g. from string functionals of the Nambu-Schild-Eguchi type. Although these models belong to the nonrenormalizable class of quantum field theories, we prove finiteness for a rectangular string shape up to three loop level, for circular boundary up to two loop order, and for a variety of graphs in higher order, thus indicating that the result might hold in general. From the explicit calculation of the two loop approximation we extract the first model dependent corrections to the qanti q - potential or the Casimir effect. The importance of dilation transformations for the properties of the renormalization procedure are investigated. We prove that under certain conditions, forced by symmetry properties, the association of finite values to divergent series is unique, independent of the regularization procedure. (orig.)

Renormalization of the nonlinear O(3) model with θ-term

Energy Technology Data Exchange (ETDEWEB)

Flore, Raphael, E-mail: raphael.flore@uni-jena.de [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena (Germany)

2013-05-11

The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite multiplicative renormalization occurs in the extreme infrared. In order to compute the effects of the zero modes, a specific representation of the Clifford algebra is developed which allows to reformulate the bosonic problem in terms of Dirac operators and to employ the index theorem.

Holographic renormalization and supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Genolini, Pietro Benetti [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom); Cassani, Davide [LPTHE, Sorbonne Universités UPMC Paris 6 and CNRS, UMR 7589,F-75005, Paris (France); Martelli, Dario [Department of Mathematics, King’s College London,The Strand, London, WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom)

2017-02-27

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N=2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.

Holographic Renormalization in Dense Medium

International Nuclear Information System (INIS)

Park, Chanyong

2014-01-01

The holographic renormalization of a charged black brane with or without a dilaton field, whose dual field theory describes a dense medium at finite temperature, is investigated in this paper. In a dense medium, two different thermodynamic descriptions are possible due to an additional conserved charge. These two different thermodynamic ensembles are classified by the asymptotic boundary condition of the bulk gauge field. It is also shown that in the holographic renormalization regularity of all bulk fields can reproduce consistent thermodynamic quantities and that the Bekenstein-Hawking entropy is nothing but the renormalized thermal entropy of the dual field theory. Furthermore, we find that the Reissner-Nordström AdS black brane is dual to a theory with conformal matter as expected, whereas a charged black brane with a nontrivial dilaton profile is mapped to a theory with nonconformal matter although its leading asymptotic geometry still remains as AdS space

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.

Finite cluster renormalization group for disordered two-dimensional systems

International Nuclear Information System (INIS)

El Kenz, A.

1987-09-01

A new type of renormalization group theory using the generalized Callen identities is exploited in the study of the disordered systems. Bond diluted and frustrated Ising systems on a square lattice are analyzed with this new scheme. (author). 9 refs, 2 figs, 2 tabs

Temperature renormalization group approach to spontaneous symmetry breaking

International Nuclear Information System (INIS)

Manesis, E.; Sakakibara, S.

1985-01-01

We apply renormalization group equations that describe the finite-temperature behavior of Green's functions to investigate thermal properties of spontaneous symmetry breaking. Specifically, in the O(N).O(N) symmetric model we study the change of symmetry breaking patterns with temperature, and show that there always exists the unbroken symmetry phase at high temperature, modifying the naive result of leading order in finite-temperature perturbation theory. (orig.)

NLO renormalization in the Hamiltonian truncation

Science.gov (United States)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

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

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.

Complex-mass shell renormalization of the higher-derivative electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Turcati, Rodrigo [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Universidade Federal do Espirito Santo, Departamento de Fisica e Quimica, Vitoria, ES (Brazil); Laboratorio de Fisica Experimental (LAFEX), Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro (Brazil); Neves, Mario Junior [Universidade Federal Rural do Rio de Janeiro, Departamento de Fisica, Rio de Janeiro (Brazil)

2016-08-15

We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron-positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed. (orig.)

The renormalization scale-setting problem in QCD

Energy Technology Data Exchange (ETDEWEB)

Wu, Xing-Gang [Chongqing Univ. (China); Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mojaza, Matin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Southern Denmark, Odense (Denmark)

2013-09-01

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending

Renormalization in the stochastic quantization of field theories

International Nuclear Information System (INIS)

Brunelli, J.C.

1991-01-01

In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)

Renormalization of self-consistent Schwinger-Dyson equations at finite temperature

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2002-01-01

We show that Dyson resummation schemes based on Baym's Φ-derivable approximations can be renormalized with counter term structures solely defined on the vacuum level. First applications to the self-consistent solution of the sunset self-energy in φ 4 -theory are presented. (orig.)

Quantum renormalization group approach to geometric phases in spin chains

International Nuclear Information System (INIS)

Jafari, R.

2013-01-01

A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size

Physical renormalization condition for de Sitter QED

Science.gov (United States)

Hayashinaka, Takahiro; Xue, She-Sheng

2018-05-01

We considered a new renormalization condition for the vacuum expectation values of the scalar and spinor currents induced by a homogeneous and constant electric field background in de Sitter spacetime. Following a semiclassical argument, the condition named maximal subtraction imposes the exponential suppression on the massive charged particle limit of the renormalized currents. The maximal subtraction changes the behaviors of the induced currents previously obtained by the conventional minimal subtraction scheme. The maximal subtraction is favored for a couple of physically decent predictions including the identical asymptotic behavior of the scalar and spinor currents, the removal of the IR hyperconductivity from the scalar current, and the finite current for the massless fermion.

Stochastic quantization of fermionic theories: renormalization of the massive Thirring model

Energy Technology Data Exchange (ETDEWEB)

Brunelli, J C

1992-10-01

Using the Langevin approach for stochastic processes we study the renormalizability of the massive Thirring model. At finite fictitious time, we prove the absence of induced quadrilinear counterterms by verifying the cancellation of the divergencies of graphs with four external lines. This implies that the vanishing of the renormalization group beta function already occurs at finite times. (author). 12 refs., 3 figs.

Hopf-algebraic renormalization of QED in the linear covariant gauge

Energy Technology Data Exchange (ETDEWEB)

Kißler, Henry, E-mail: kissler@physik.hu-berlin.de

2016-09-15

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

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.)

Renormalization group analysis of the temperature dependent coupling constant in massless theory

International Nuclear Information System (INIS)

Yamada, Hirofumi.

1987-06-01

A general analysis of finite temperature renormalization group equations for massless theories is presented. It is found that in a direction where momenta and temperature are scaled up with their ratio fixed the coupling constant behaves in the same manner as in zero temperature and that asymptotic freedom at short distances is also maintained at finite temperature. (author)

Renormalization of Hamiltonians

International Nuclear Information System (INIS)

Glazek, S.D.; Wilson, K.G.

1993-01-01

This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method

A perturbative study of two four-quark operators in finite volume renormalization schemes

CERN Document Server

Palombi, Filippo; Sint, S

2006-01-01

Starting from the QCD Schroedinger functional (SF), we define a family of renormalization schemes for two four-quark operators, which are, in the chiral limit, protected against mixing with other operators. With the appropriate flavour assignments these operators can be interpreted as part of either the $\\Delta F=1$ or $\\Delta F=2$ effective weak Hamiltonians. In view of lattice QCD with Wilson-type quarks, we focus on the parity odd components of the operators, since these are multiplicatively renormalized both on the lattice and in continuum schemes. We consider 9 different SF schemes and relate them to commonly used continuum schemes at one-loop order of perturbation theory. In this way the two-loop anomalous dimensions in the SF schemes can be inferred. As a by-product of our calculation we also obtain the one-loop cutoff effects in the step-scaling functions of the respective renormalization constants, for both O(a) improved and unimproved Wilson quarks. Our results will be needed in a separate study of ...

Finiteness of PST self-dual models

International Nuclear Information System (INIS)

Del Cima, Oswaldo M.; Piguet, Olivier; Sarandy, Marcelo S.

2000-12-01

The Pasti-Sorokin-Tonin model for describing chiral forms is considered at the quantum level. We study the ultraviolet and infrared behaviour of the model in two, four and six dimensions in the framework of algebraic renormalization. The absence of anomalies, as well as the finiteness, up to non-physical renormalizations, are shown in all dimensions analyzed. (author)

The Implementation of the Renormalized Complex MSSM in FeynArts and FormCalc

CERN Document Server

Fritzsche, T; Heinemeyer, S; Rzehak, H; Schappacher, C

2014-01-01

We describe the implementation of the renormalized complex MSSM (cMSSM) in the diagram generator FeynArts and the calculational tool FormCalc. This extension allows to perform UV-finite one-loop calculations of cMSSM processes almost fully automatically. The Feynman rules for the cMSSM with counterterms are available as a new model file for FeynArts. Also included are default definitions of the renormalization constants; this fixes the renormalization scheme. Beyond that all model parameters are generic, e.g. we do not impose any relations to restrict the number of input parameters. The model file has been tested extensively for several non-trivial decays and scattering reactions. Our renormalization scheme has been shown to give stable results over large parts of the cMSSM parameter space.

Excited state TBA and renormalized TCSA in the scaling Potts model

Science.gov (United States)

Lencsés, M.; Takács, G.

2014-09-01

We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.

Renormalization of Supersymmetric QCD on the Lattice

Science.gov (United States)

Costa, Marios; Panagopoulos, Haralambos

2018-03-01

We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review

Science.gov (United States)

Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

2015-12-01

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme—this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the ‘principle of maximum conformality’ (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the ‘principle of minimum sensitivity’ (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R e+e- and Γ(H\\to b\\bar{b}) up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on

$\\delta$-Expansion at Finite Temperature

OpenAIRE

Ramos, Rudnei O.

1996-01-01

We apply the $\\delta$-expansion perturbation scheme to the $\\lambda \\phi^{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\\delta$-expansion the interaction term is written as $\\lambda (\\phi^{2})^{ 1 + \\delta}$ and $\\delta$ is considered as the perturbation parameter. We compute within this perturbative approach the renormalized mass at finite temperature at a finite order in $\\delta$. The results are compared with the usual loop-expansion at finite temperature.

Finiteness of quantum field theories and supersymmetry

International Nuclear Information System (INIS)

Lucha, W.; Neufeld, H.

1986-01-01

We study the consequences of finiteness for a general renormalizable quantum field theory by analysing the finiteness conditions resulting from the requirement of absence of divergent contributions to the renormalizations of the parameters of an arbitrary gauge theory. In all cases considered, the well-known two-loop finite supersymmetric theories prove to be the unique solution of the finiteness criterion. (Author)

Dynamical renormalization group approach to relaxation in quantum field theory

International Nuclear Information System (INIS)

Boyanovsky, D.; Vega, H.J. de

2003-01-01

The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths

Toward finite quantum field theories

International Nuclear Information System (INIS)

Rajpoot, S.; Taylor, J.G.

1986-01-01

The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)

Renormalization of loop functions for all loops

International Nuclear Information System (INIS)

Brandt, R.A.; Neri, F.; Sato, M.

1981-01-01

It is shown that the vacuum expectation values W(C 1 ,xxx, C/sub n/) of products of the traces of the path-ordered phase factors P exp[igcontour-integral/sub C/iA/sub μ/(x)dx/sup μ/] are multiplicatively renormalizable in all orders of perturbation theory. Here A/sub μ/(x) are the vector gauge field matrices in the non-Abelian gauge theory with gauge group U(N) or SU(N), and C/sub i/ are loops (closed paths). When the loops are smooth (i.e., differentiable) and simple (i.e., non-self-intersecting), it has been shown that the generally divergent loop functions W become finite functions W when expressed in terms of the renormalized coupling constant and multiplied by the factors e/sup -K/L(C/sub i/), where K is linearly divergent and L(C/sub i/) is the length of C/sub i/. It is proved here that the loop functions remain multiplicatively renormalizable even if the curves have any finite number of cusps (points of nondifferentiability) or cross points (points of self-intersection). If C/sub γ/ is a loop which is smooth and simple except for a single cusp of angle γ, then W/sub R/(C/sub γ/) = Z(γ)W(C/sub γ/) is finite for a suitable renormalization factor Z(γ) which depends on γ but on no other characteristic of C/sub γ/. This statement is made precise by introducing a regularization, or via a loop-integrand subtraction scheme specified by a normalization condition W/sub R/(C-bar/sub γ/) = 1 for an arbitrary but fixed loop C-bar/sub γ/. Next, if C/sub β/ is a loop which is smooth and simple except for a cross point of angles β, then W(C/sub β/) must be renormalized together with the loop functions of associated sets S/sup i//sub β/ = ]C/sup i/ 1 ,xxx, C/sup i//sub p/i] (i = 2,xxx,I) of loops C/sup i//sub q/ which coincide with certain parts of C/sub β/equivalentC 1 1 . Then W/sub R/(S/sup i//sub β/) = Z/sup i/j(β)W(S/sup j//sub β/) is finite for a suitable matrix Z/sup i/j

Effective-field renormalization-group method for Ising systems

Science.gov (United States)

Fittipaldi, I. P.; De Albuquerque, D. F.

1992-02-01

A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.

A simple method for one-loop renormalization in curved space-time

Energy Technology Data Exchange (ETDEWEB)

Markkanen, Tommi [Helsinki Institute of Physics and Department of Physics, P.O. Box 64, FI-00014, University of Helsinki (Finland); Tranberg, Anders, E-mail: tommi.markkanen@helsinki.fi, E-mail: anders.tranberg@uis.no [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen (Denmark)

2013-08-01

We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.

Supersymmetry at finite temperature

International Nuclear Information System (INIS)

Clark, T.E.; Love, S.T.

1983-01-01

Finite-temperature supersymmetry (SUSY) is characterized by unbroken Ward identities for SUSY variations of ensemble averages of Klein-operator inserted imaginary time-ordered products of fields. Path-integral representations of these products are defined and the Feynman rules in superspace are given. The finite-temperature no-renormalization theorem is derived. Spontaneously broken SUSY at zero temperature is shown not to be restored at high temperature. (orig.)

Cook-Levin Theorem Algorithmic-Reducibility/Completeness = Wilson Renormalization-(Semi)-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') REPLACING CRUTCHES!!!: Models: Turing-machine, finite-state-models, finite-automata

Science.gov (United States)

Young, Frederic; Siegel, Edward

Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!

Functional renormalization group approach to interacting three-dimensional Weyl semimetals

Science.gov (United States)

Sharma, Anand; Scammell, Arthur; Krieg, Jan; Kopietz, Peter

2018-03-01

We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes—cutoff in fermionic or bosonic propagators—in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavskiĭ [Sov. Phys. JETP 32, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.

DeWitt-Schwinger renormalization and vacuum polarization in d dimensions

International Nuclear Information System (INIS)

Thompson, R. T.; Lemos, Jose P. S.

2009-01-01

Calculation of the vacuum polarization, 2 (x)>, and expectation value of the stress tensor, μν (x)>, has seen a recent resurgence, notably for black hole spacetimes. To date, most calculations of this type have been done only in four dimensions. Extending these calculations to d dimensions includes d-dimensional renormalization. Typically, the renormalizing terms are found from Christensen's covariant point splitting method for the DeWitt-Schwinger expansion. However, some manipulation is required to put the correct terms into a form that is compatible with problems of the vacuum polarization type. Here, after a review of the current state of affairs for 2 (x)> and μν (x)> calculations and a thorough introduction to the method of calculating 2 (x)>, a compact expression for the DeWitt-Schwinger renormalization terms suitable for use in even-dimensional spacetimes is derived. This formula should be useful for calculations of 2 (x)> and μν (x)> in even dimensions, and the renormalization terms are shown explicitly for four and six dimensions. Furthermore, use of the finite terms of the DeWitt-Schwinger expansion as an approximation to 2 (x)> for certain spacetimes is discussed, with application to four and five dimensions.

Point transformations and renormalization in the unitary gauge. III. Renormalization effects

International Nuclear Information System (INIS)

Sherry, T.N.

1976-06-01

An analysis of two simple gauge theory models is continued using point transformations rather than gauge transformations. The renormalization constants are examined directly in two gauges, the renormalization (Landau) and unitary gauges. The result is that the individual coupling constant renormalizations are identical when calculated in each of the above two gauges, although the wave-function and proper vertex renormalizations differ

Features of finite quantum field theories

International Nuclear Information System (INIS)

Boehm, M.; Denner, A.

1987-01-01

We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)

Finite quantum field theories

International Nuclear Information System (INIS)

Lucha, W.; Neufeld, H.

1986-01-01

We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.

Science.gov (United States)

Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2012-07-01

We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime

International Nuclear Information System (INIS)

Leen, T.K.

1983-01-01

In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identifies. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space

One-loop renormalization of Resonance Chiral Theory: scalar and pseudoscalar resonances

International Nuclear Information System (INIS)

Rosell, Ignasi; Ruiz-FemenIa, Pedro; Portoles, Jorge

2005-01-01

We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its β-function at one-loop with the use of the background field method. Thus we also provide the full set of operators that renormalize the theory at one loop and render it finite

Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

Science.gov (United States)

Bischoff, Jan-Moritz; Jeckelmann, Eric

2017-11-01

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

Algebraic renormalization. Perturbative renormalization, symmetries and anomalies

International Nuclear Information System (INIS)

Piguet, O.

1995-01-01

This book is an introduction to the algebraic method in the perturbative renormalization of relativistic quantum field theory. After a general introduction to renormalized perturbation theory the quantum action principle and Ward identities are described. Then Yang-Mills gauge theories are considered. Thereafter the BRS cohomology and descent equations are described. Then nonrenormalization theorems and topological field theories are considered. Finally an application to the bosonic string is described. (HSI)

Neutrix calculus and finite quantum field theory

International Nuclear Information System (INIS)

Ng, Y Jack; Dam, H van

2005-01-01

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like quantum electrodynamics are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT, obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework. (letter to the editor)

The Kadanoff lower-bound variational renormalization group applied to an SU(2) lattice spin model

International Nuclear Information System (INIS)

Thorleifsson, G.; Damgaard, P.H.

1990-07-01

We apply the variational lower-bound Renormalization Group transformation of Kadanoff to an SU(2) lattice spin model in 2 and 3 dimensions. Even in the one-hypercube framework of this renormalization group transformation the present model is characterised by having an infinite basis of fundamental operators. We investigate whether the lower-bound variational renormalization group transformation yields results stable under truncations of this operator basis. Our results show that for this particular spin model this is not the case. (orig.)

Renormalization and radiative corrections to masses in a general Yukawa model

Science.gov (United States)

Fox, M.; Grimus, W.; Löschner, M.

2018-01-01

We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields φa, general Yukawa couplings and a ℤ4 symmetry that forbids linear and trilinear terms in the scalar potential. Moreover, fermions become massive only after spontaneous symmetry breaking of the ℤ4 symmetry by vacuum expectation values (VEVs) of the φa. Introducing the shifted fields ha whose VEVs vanish, MS¯ renormalization of the parameters of the unbroken theory suffices to make the theory finite. However, in this way, beyond tree level it is necessary to perform finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, in order to ensure vanishing one-point functions of the ha. Moreover, adapting the renormalization scheme to a situation with many scalars and VEVs, we consider the physical fermion and scalar masses as derived quantities, i.e. as functions of the coupling constants and VEVs. Consequently, the masses have to be computed order by order in a perturbative expansion. In this scheme, we compute the self-energies of fermions and bosons and show how to obtain the respective one-loop contributions to the tree-level masses. Furthermore, we discuss the modification of our results in the case of Dirac fermions and investigate, by way of an example, the effects of a flavor symmetry group.

Renormalization-scheme-invariant QCD and QED: The method of effective charges

International Nuclear Information System (INIS)

Grunberg, G.

1984-01-01

We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding Stueckelberg--Peterman--Gell-Mann--Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter Λ, even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass m is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QED is discussed as an example of an extension of the method to problems involving several momentum scales

Renormalization of the three-boson system with short-range interactions revisited

International Nuclear Information System (INIS)

Epelbaum, E.; Gegelia, J.; Meissner, Ulf G.; Yao, De-Liang

2017-01-01

We consider renormalization of the three-body scattering problem in low-energy effective field theory of self-interacting scalar particles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation. The obtained leading-order equation is perturbatively renormalizable and non-perturbatively finite and does not require a three-body counter term in contrast to its non-relativistic approximation. (orig.)

Dimensional renormalization and comparison of renormalization schemes in quantum electrodynamics

International Nuclear Information System (INIS)

Coquereaux, R.

1979-02-01

The method of dimensional renormalization as applied to quantum electrodynamics is discussed. A general method is given which allows one to compare the various quantities like coupling constants and masses that appear in different renormalization schemes

The O(N) model at nonzero temperature: renormalization of the gap equations in Hartree and large-N approximations

International Nuclear Information System (INIS)

Lenaghan, J.T.; Rischke, D.H.

2000-01-01

The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N ) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest. (author)

Phase diagram of the Hubbard model with arbitrary band filling: renormalization group approach

International Nuclear Information System (INIS)

Cannas, Sergio A.; Cordoba Univ. Nacional; Tsallis, Constantino.

1991-01-01

The finite temperature phase diagram of the Hubbard model in d = 2 and d = 3 is calculated for arbitrary values of the parameter U/t and chemical potential μ using a quantum real space renormalization group. Evidence for a ferromagnetic phase at low temperatures is presented. (author). 15 refs., 5 figs

Clifford algebra in finite quantum field theories

International Nuclear Information System (INIS)

Moser, M.

1997-12-01

We consider the most general power counting renormalizable and gauge invariant Lagrangean density L invariant with respect to some non-Abelian, compact, and semisimple gauge group G. The particle content of this quantum field theory consists of gauge vector bosons, real scalar bosons, fermions, and ghost fields. We assume that the ultimate grand unified theory needs no cutoff. This yields so-called finiteness conditions, resulting from the demand for finite physical quantities calculated by the bare Lagrangean. In lower loop order, necessary conditions for finiteness are thus vanishing beta functions for dimensionless couplings. The complexity of the finiteness conditions for a general quantum field theory makes the discussion of non-supersymmetric theories rather cumbersome. Recently, the F = 1 class of finite quantum field theories has been proposed embracing all supersymmetric theories. A special type of F = 1 theories proposed turns out to have Yukawa couplings which are equivalent to generators of a Clifford algebra representation. These algebraic structures are remarkable all the more than in the context of a well-known conjecture which states that finiteness is maybe related to global symmetries (such as supersymmetry) of the Lagrangean density. We can prove that supersymmetric theories can never be of this Clifford-type. It turns out that these Clifford algebra representations found recently are a consequence of certain invariances of the finiteness conditions resulting from a vanishing of the renormalization group β-function for the Yukawa couplings. We are able to exclude almost all such Clifford-like theories. (author)

Distribution of the minimum path on percolation clusters: A renormalization group calculation

International Nuclear Information System (INIS)

Hipsh, Lior.

1993-06-01

This thesis uses the renormalization group for the research of the chemical distance or the minimal path on percolation clusters on a 2 dimensional square lattice. Our aims are to calculate analytically (iterative calculation) the fractal dimension of the minimal path. d min. , and the distributions of the minimum paths, l min for different lattice sizes and for different starting densities (including the threshold value p c ). For the distributions. We seek for an analytic form which describes them. The probability to get a minimum path for each linear size L is calculated by iterating the distribution of l min for the basic cell of size 2*2 to the next scale sizes, using the H cell renormalization group. For the threshold value of p and for values near to p c . We confirm a scaling in the form: P(l,L) =f1/l(l/(L d min ). L - the linear size, l - the minimum path. The distribution can be also represented in the Fourier space, so we will try to solve the renormalization group equations in this space. A numerical fitting is produced and compared to existing numerical results. In order to improve the agreement between the renormalization group and the numerical simulations, we also present attempts to generalize the renormalization group by adding more parameters, e.g. correlations between bonds in different directions or finite densities for occupation of bonds and sites. (author) 17 refs

Functional renormalization group methods in quantum chromodynamics

International Nuclear Information System (INIS)

Braun, J.

2006-01-01

We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

Functional renormalization group methods in quantum chromodynamics

Energy Technology Data Exchange (ETDEWEB)

Braun, J.

2006-12-18

We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

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

Phase structure of NJL model with weak renormalization group

Science.gov (United States)

Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

2018-06-01

We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Matrix product density operators: Renormalization fixed points and boundary theories

Energy Technology Data Exchange (ETDEWEB)

Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)

2017-03-15

We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).

Renormalization and effective lagrangians

International Nuclear Information System (INIS)

Polchinski, J.

1984-01-01

There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional lambda PHI 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed. (orig.)

One-loop Renormalization of Resonance Chiral Theory with Scalar and Pseudoscalar Resonances

International Nuclear Information System (INIS)

Rosell, I.

2007-01-01

The divergent part of the generating functional of the Resonance Chiral Theory is evaluated up to one loop when one multiplet of scalar and pseudoscalar resonances are included and interaction terms which couple up to two resonances are considered. Hence we obtain the renormalization of the couplings of the initial Lagrangian and, moreover, the complete list of operators that make this theory finite, at this order

Physical renormalization schemes and asymptotic safety in quantum gravity

Science.gov (United States)

Falls, Kevin

2017-12-01

The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.

Algebraic renormalization of parity-preserving QED3 coupled to scalar matter II: broken case

International Nuclear Information System (INIS)

Cima, O.M. del; Franco, D.H.T.; Helayel-Neto, J.A.; Piguet, O.

1996-11-01

In this letter the algebraic renormalization method, which is independent of any kind of regularization scheme, is presented for the parity-preserving QED 3 coupled to scalar matter in the broken regime, where the scalar assumes a finite vacuum expectation value, =v. The model shows to be stable under radiative corrections and anomaly free. (author)

Variational solution of the Gross-Neveu model; 2, finite-N and renormalization

CERN Document Server

Arvanitis, C; Iacomi, M; Kneur, J L; Neveu, A

1995-01-01

We show how to perform systematically improvable variational calculations in the O(2N) Gross-Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the renormalization group. The final point is a general framework for the calculation of non-perturbative quantities like condensates, masses, etc..., in an asymptotically free field theory. For the Gross-Neveu model, the numerical results obtained from a "two-loop" variational calculation are in very good agreement with exact quantities down to low values of N.

Introduction to the functional renormalization group

International Nuclear Information System (INIS)

Kopietz, Peter; Bartosch, Lorenz; Schuetz, Florian

2010-01-01

This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics. (orig.)

Renormalization of the Abelian–Higgs model in the Rξ and Unitary gauges and the physicality of its scalar potential

Directory of Open Access Journals (Sweden)

Nikos Irges

2017-11-01

Full Text Available We perform an old school, one-loop renormalization of the Abelian–Higgs model in the Unitary and Rξ gauges, focused on the scalar potential and the gauge boson mass. Our goal is to demonstrate in this simple context the validity of the Unitary gauge at the quantum level, which could open the way for an until now (mostly avoided framework for loop computations. We indeed find that the Unitary gauge is consistent and equivalent to the Rξ gauge at the level of β-functions. Then we compare the renormalized, finite, one-loop Higgs potential in the two gauges and we again find equivalence. This equivalence needs not only a complete cancellation of the gauge fixing parameter ξ from the Rξ gauge potential but also requires its ξ-independent part to be equal to the Unitary gauge result. We follow the quantum behavior of the system by plotting Renormalization Group trajectories and Lines of Constant Physics, with the former the well known curves and with the latter, determined by the finite parts of the counter-terms, particularly well suited for a comparison with non-perturbative studies.

Renormalization ambiguities and conformal anomaly in metric-scalar backgrounds

International Nuclear Information System (INIS)

Asorey, M.; Berredo-Peixoto, G. de; Shapiro, I. L.

2006-01-01

We analyze the problem of the existing ambiguities in the conformal anomaly in theories with an external scalar field in curved backgrounds. In particular, we consider the anomaly of a self-interacting massive scalar field theory and of a Yukawa model in the massless conformal limit. In all cases the ambiguities are related to finite renormalizations of local nonminimal terms in the effective action. We point out the generic nature of this phenomenon and provide a general method to identify the theories where such an ambiguity can arise

Renormalization group and asymptotic freedom

International Nuclear Information System (INIS)

Morris, J.R.

1978-01-01

Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions

A confining and asymptotically free solution for the renormalization group invariant charge

International Nuclear Information System (INIS)

Kellett, B.H.

1978-01-01

The central role of the invariant charge in applications of the renormalization group to quantum chromodynamics is discussed. The general structure of the invariant charge is examined, and it is shown to be a non-singular function of q 2 for all finite non-zero q 2 . At q 2 = 0 and q 2 = +or- infinity shows that QCD is asymptotically free. Some applications of these general results are discussed

Finite-size scaling in two-dimensional superfluids

International Nuclear Information System (INIS)

Schultka, N.; Manousakis, E.

1994-01-01

Using the x-y model and a nonlocal updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two-dimensional superfluid on large-size square lattices LxL up to 400x400. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of L values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization-group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson renormalization group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments

Unambiguity of renormalization group calculations in QCD

International Nuclear Information System (INIS)

Vladimirov, A.A.

1979-01-01

A detailed analysis of the reduction of ambiguities determined by an arbitrary renormalization scheme is presented for the renormalization group calculations of physical quantities in quantum chromodynamics (QCD). Some basic formulas concerning the renormalization-scheme dependence of Green's and renormalization group functions are given. A massless asymptotically free theory with one coupling constant g is considered. In conclusion, several rules for renormalization group calculations in QCD are formulated

Hadamard and minimal renormalizations

International Nuclear Information System (INIS)

Castagnino, M.A.; Gunzig, E.; Nardone, P.; Paz, J.P.

1986-01-01

A common language is introduced to study two, well-known, different methods for the renormalization of the energy-momentum tensor of a scalar neutral quantum field in curved space-time. Different features of the two renormalizations are established and compared

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)

Determination of the ultimate load in concrete slabs by the yield line finite element method

International Nuclear Information System (INIS)

Vaz, L.E.; Feijo, B.; Martha, L.F.R.; Lopes, M.M.

1984-01-01

A method for calculating the ultimate load in reinforced concrete slabs is proposed. The method follows the finite element aproach representating the continuum slab as an assembly of rigid triangular plates connected along their sides through yield line elements. This approach leads to the definition of the displacement configuration of the plate only as a function of the transversal displacement at the nodes of the mesh (1 DOF per node) reducing significantly the number of DOF's in relation to the conventional formulation by means of the finite element method (minimum of 3 DOF per node). Nonlinear behaviour of the reinforced concrete section is considered in the definition of the moment rotation curve of the yield lines. The effect of the in plane forces acting in the middle surface of the plate is also taken into account. The validity of the model is verified comparing the numerical solutions with the results of the classical yield line theory. (Author) [pt

The analytic renormalization group

Directory of Open Access Journals (Sweden)

Frank Ferrari

2016-08-01

Full Text Available Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0, together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.

Renormalization Group Theory

International Nuclear Information System (INIS)

Stephens, C. R.

2006-01-01

In this article I give a brief account of the development of research in the Renormalization Group in Mexico, paying particular attention to novel conceptual and technical developments associated with the tool itself, rather than applications of standard Renormalization Group techniques. Some highlights include the development of new methods for understanding and analysing two extreme regimes of great interest in quantum field theory -- the ''high temperature'' regime and the Regge regime

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

Energy Technology Data Exchange (ETDEWEB)

Chankowski, Piotr H. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Lewandowski, Adrian [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Meissner, Krzysztof A. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland)

2016-11-18

We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional (MS)-bar scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the (MS)-bar scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

Similarity renormalization group evolution of N N interactions within a subtractive renormalization scheme

Directory of Open Access Journals (Sweden)

Durães F.O.

2010-04-01

Full Text Available We apply the similarity renormalization group (SRG approach to evolve a nucleon-nucleon (N N interaction in leading-order (LO chiral effective field theory (ChEFT, renormalized within the framework of the subtracted kernel method (SKM. We derive a fixed-point interaction and show the renormalization group (RG invariance in the SKM approach. We also compare the evolution of N N potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS equation and the evolution with the similarity cutoff through the SRG transformation.

Compositeness condition in the renormalization group equation

International Nuclear Information System (INIS)

Bando, Masako; Kugo, Taichiro; Maekawa, Nobuhiro; Sasakura, Naoki; Watabiki, Yoshiyuki; Suehiro, Kazuhiko

1990-01-01

The problems in imposing compositeness conditions as boundary conditions in renormalization group equations are discussed. It is pointed out that one has to use the renormalization group equation directly in cutoff theory. In some cases, however, it can be approximated by the renormalization group equation in continuum theory if the mass dependent renormalization scheme is adopted. (orig.)

Modification of the ''Coulomb'' interaction at small distances in finite quantum electrodynamics

International Nuclear Information System (INIS)

Manoukian, E.B.

1982-01-01

We investigate the ''Coulomb'' interaction in finite QED at small distances. By finite QED it is meant that we sum all photon self-energy subgraphs in renormalized QED and fix α, the renormalized fine-structure constant, as the (infinite order) zero of the Callan-Symanzik function: β(α) = 0/sup infinity/. We show that for mcVertical Barx-x 'Vertical Bar/h 1 and e 2 at x and x ', respectively, is given by V(Vertical Barx-x'Vertical Bar)approx. =(e 1 e 2 / 4πVertical Barx-x'Vertical Bar) [q 1 (α)-q 2 (α)mcVertical Barx-x'Vertical Bar / h+O(m 2 c 2 Vertical Barx-x'Vertical Bar 2 /h 2 )], where 1 1 (α) 2 (α)< infinity

Fixed point of the parabolic renormalization operator

CERN Document Server

Lanford III, Oscar E

2014-01-01

This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.   Inside, readers will find a detailed introduction into the theory of parabolic bifurcation,  Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.   The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...

Finite N=1 SUSY gauge field theories

International Nuclear Information System (INIS)

Kazakov, D.I.

1986-01-01

The authors give a detailed description of the method to construct finite N=1 SUSY gauge field theories in the framework of N=1 superfields within dimensional regularization. The finiteness of all Green functions is based on supersymmetry and gauge invariance and is achieved by a proper choice of matter content of the theory and Yukawa couplings in the form Y i =f i (ε)g, where g is the gauge coupling, and the function f i (ε) is regular at ε=0 and is calculated in perturbation theory. Necessary and sufficient conditions for finiteness are determined already in the one-loop approximation. The correspondence with an earlier proposed approach to construct finite theories based on aigenvalue solutions of renormalization-group equations is established

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

Science.gov (United States)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

Extending the random-phase approximation for electronic correlation energies: the renormalized adiabatic local density approximation

DEFF Research Database (Denmark)

Olsen, Thomas; Thygesen, Kristian S.

2012-01-01

The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces...... while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...

Renormalized Lie perturbation theory

International Nuclear Information System (INIS)

Rosengaus, E.; Dewar, R.L.

1981-07-01

A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another

Charge transport properties of a twisted DNA molecule: A renormalization approach

Energy Technology Data Exchange (ETDEWEB)

Almeida, M.L. de; Ourique, G.S.; Fulco, U.L. [Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil); Albuquerque, E.L., E-mail: eudenilson@gmail.com [Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil); Moura, F.A.B.F. de; Lyra, M.L. [Instituto de Física, Universidade Federal de Alagoas, 57072-900 Maceió-AL (Brazil)

2016-10-20

In this work we study the charge transport properties of a nanodevice consisting of a finite segment of the DNA molecule sandwiched between two metallic electrodes. Our model takes into account a nearest-neighbor tight-binding Hamiltonian considering the nucleobases twist motion, whose solutions make use of a two-steps renormalization process to simplify the algebra, which can be otherwise quite involved. The resulting variations of the charge transport efficiency are analyzed by numerically computing the main features of the electron transmittance spectra as well as their I × V characteristic curves.

On renormalization of axial anomaly

International Nuclear Information System (INIS)

Efremov, A.V.; Teryaev, O.V.

1989-01-01

It is shown that multiplicative renormalization of the axial singlet current results in renormalization of the axial anomaly in all orders of perturbation theory. It is a necessary condition for the Adler - Bardeen theorem being valid. 10 refs.; 2 figs

Renormalization of self-consistent approximation schemes at finite temperature. II. Applications to the sunset diagram

International Nuclear Information System (INIS)

Hees, Hendrik van; Knoll, Joern

2002-01-01

The theoretical concepts for the renormalization of self-consistent Dyson resummations, devised in the first paper of this series, are applied to first example cases of φ 4 theory. In addition to the tadpole (Hartree) approximation, as a novel part the numerical solutions are presented, which include the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or the two-particle irreducible effective action concept

Renormalization of self-consistent approximation schemes at finite temperature II: applications to the sunset diagram

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2001-01-01

The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept. (orig.)

Renormalization group flow of scalar models in gravity

International Nuclear Information System (INIS)

Guarnieri, Filippo

2014-01-01

In this Ph.D. thesis we study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Horava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson's renormalization group. In particular we quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω=0 in the local potential approximation. Finally, we investigate, using a perturbative RG scheme, the asymptotic freedom of the Horava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton's constant to a marginal coupling and explicitly preserves unitarity. In particular we evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.

Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

Directory of Open Access Journals (Sweden)

Huan-Yu Bi

2015-09-01

Full Text Available The Principle of Maximum Conformality (PMC eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I; the other, more recent, method (PMC-II uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e− and the Higgs partial width Γ(H→bb¯. Both methods lead to the same resummed (‘conformal’ series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi}-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

The Obstruction criterion for non existence of Invariant Circles and Renormalization.

CERN Document Server

De la Llave, R

2003-01-01

We formulate a conjecture which supplements the standard renormalization scenario for the breakdown of golden circle in twist maps. We show rigorously that if the conjecture was true then: a) The stable manifold of the non-trivial fixed point would indeed be a boundary between the existence of smooth invariant tori and hyperbolic orbits with golden mean rotation number. In particular, the boundary of the set of twist maps with a torus with a golden mean rotation number would include a smooth submanifold in the space of analytic mappings. b) The obstruction criterion of [Olvera-Simo] would be sharp in the universality class of the renormalization group. c) The criterion of [Greene-79] for existence of invariant circles if and only if there the residues of approximating orbits are finite would be valid for maps in the universality class. d) If there is no invariant circle, there are hyperbolic sets with golden mean rotation number. We also provide numerical evidence which suggests that the conjecture is true an...

Quantum phase transition by employing trace distance along with the density matrix renormalization group

International Nuclear Information System (INIS)

Luo, Da-Wei; Xu, Jing-Bo

2015-01-01

We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs

Numerical investigation of renormalization group equations in a model of vector field advected by anisotropic stochastic environment

International Nuclear Information System (INIS)

Busa, J.; Ajryan, Eh.A.; Jurcisinova, E.; Jurcisin, M.; Remecky, R.

2009-01-01

Using the field-theoretic renormalization group, the influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of passive transverse vector field advected by an incompressible turbulent flow is investigated. The velocity field is taken to have a Gaussian statistics with zero mean and defined noise with finite time correlations. It is shown that the inertial-range scaling regimes are given by the existence of infrared stable fixed points of the corresponding renormalization group equations with some angle integrals. The analysis of integrals is given. The problem is solved numerically and the borderline spatial dimension d e (1,3] below which the stability of the scaling regime is not present is found as a function of anisotropy parameters

Block renormalization for quantum Ising models in dimension d = 2: applications to the pure and random ferromagnet, and to the spin-glass

International Nuclear Information System (INIS)

Monthus, Cécile

2015-01-01

For the quantum Ising chain, the self-dual block renormalization procedure of Fernandez-Pacheco (1979 Phys. Rev. D 19 3173) is known to reproduce exactly the location of the zero-temperature critical point and the correlation length exponent ν = 1. Recently, Miyazaki and Nishimori (2013 Phys. Rev. E 87 032154) have proposed to study the disordered quantum Ising model in dimensions d > 1 by applying the Fernandez-Pacheco procedure successively in each direction. To avoid the inequivalence of directions of their approach, we propose here an alternative procedure where the d directions are treated on the same footing. For the pure model, this leads to the correlation length exponents ν ≃ 0.625 in d = 2 (to be compared with the 3D classical Ising model exponent ν ≃ 0.63) and ν ≃ 0.5018 (to be compared with the 4D classical Ising model mean-field exponent ν = 1/2). For the disordered model in dimension d = 2, either ferromagnetic or spin-glass, the numerical application of the renormalization rules to samples of linear size L = 4096 yields that the transition is governed by an Infinite Disorder Fixed Point, with the activated exponent ψ ≃ 0.65, the typical correlation exponent ν typ  ≃ 0.44 and the finite-size correlation exponent ν FS  ≃ 1.25. We discuss the similarities and differences with the Strong Disorder Renormalization results. (paper)

Renormalization Analysis of a Composite Ultrasonic Transducer with a Fractal Architecture

Science.gov (United States)

Algehyne, Ebrahem A.; Mulholland, Anthony J.

To ensure the safe operation of many safety critical structures such as nuclear plants, aircraft and oil pipelines, non-destructive imaging is employed using piezoelectric ultrasonic transducers. These sensors typically operate at a single frequency due to the restrictions imposed on their resonant behavior by the use of a single length scale in the design. To allow these transducers to transmit and receive more complex signals it would seem logical to use a range of length scales in the design so that a wide range of resonating frequencies will result. In this paper, we derive a mathematical model to predict the dynamics of an ultrasound transducer that achieves this range of length scales by adopting a fractal architecture. In fact, the device is modeled as a graph where the nodes represent segments of the piezoelectric and polymer materials. The electrical and mechanical fields that are contained within this graph are then expressed in terms of a finite element basis. The structure of the resulting discretized equations yields to a renormalization methodology which is used to derive expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities. A comparison with a standard design shows some benefits of these fractal designs.

Noise spectrum of quantum transport through double quantum dots: Renormalization and non-Markovian effects

Directory of Open Access Journals (Sweden)

Pengqin Shi

2016-09-01

Full Text Available Based on the time-nonlocal particle number-resolved master equation, we investigate the sequential electron transport through the interacting double quantum dots. Our calculations show that there exists the effect of energy renormalization in the dispersion of the bath interaction spectrum and it is sensitive to the the bandwidth of the bath. This effect would strongly affect the stationary current and its zero-frequency shot noise for weak inter-dot coherent coupling strength, but for strong inter-dot coupling regime, it is negligible due to the strong intrinsic Rabi coherent dynamics. Moreover, the possible observable effects of the energy renormalization in the noise spectrum are also investigated through the Rabi coherence signal. Finally, the non-Markovian effect is manifested in the finite-frequency noise spectrum with the appearance of quasisteps, and the magnitude of these quasisteps are modified by the dispersion function.

The functional renormalization group for interacting quantum systems with spin-orbit interaction

International Nuclear Information System (INIS)

Grap, Stephan Michael

2013-01-01

-Buettiker formalism from the renormalized self energy. The multi level quantum dot exhibits Kondo physics at finite Zeeman fields which can be suppressed if the field and the SOI term are not aligned in parallel. Due to broken particle hole symmetry we observed a gate voltage dependence for finite field conductance plateaus. The computed dependencies have been observed in experiments and thus highlight the flexibility of the considered model. Finally we computed the linear conductance for a multi level quantum dot model that has been proposed to describe SOI and impurity scattering effects in carbon nanotubes (CNT). The SOI was seen to affect the already complicated level structure of the CNT and thus profoundly changes the linear conductance, especially the location of conductance resonances with respect to an applied magnetic field and gate voltage. Again asymmetries influence the conductance and the effects are explained by means of the effective tunnel couplings to the eigenstates of the CNT. We finished with an improved analysis of a reduced version of this model that includes two particle vertex renormalization. The computed linear conductance is in excellent agreement with experimental data.

Golden mean renormalization for a generalized Harper equation: The Ketoja-Satija orchid

International Nuclear Information System (INIS)

Mestel, B.D.; Osbaldestin, A.H.

2004-01-01

We provide a rigorous analysis of the fluctuations of localized eigenstates in a generalized Harper equation with golden mean flux and with next-nearest-neighbor interactions. For next-nearest-neighbor interaction above a critical threshold, these self-similar fluctuations are characterized by orbits of a renormalization operator on a universal strange attractor, whose projection was dubbed the ''orchid'' by Ketoja and Satija [Phys. Rev. Lett. 75, 2762 (1995)]. We show that the attractor is given essentially by an embedding of a subshift of finite type, and give a description of its periodic orbits

Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements

DEFF Research Database (Denmark)

Clausen, Johan; Damkilde, Lars

2006-01-01

The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design...

Renormalization of supersymmetric theories

International Nuclear Information System (INIS)

Pierce, D.M.

1998-06-01

The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M W and sin 2 θ eff . He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses

Low-energy. beta. -function in a finite super-Yang-Mills model with multiple mass scales

Energy Technology Data Exchange (ETDEWEB)

Foda, O.; Helayel-Neto, J.A. (International Centre for Theoretical Physics, Trieste (Italy))

1985-02-14

We compute the one-loop contribution to the low-energy light-fermion gauge coupling in a finite supersymmetric gauge theory with two mass scales: a heavy mass that breaks an initial N=4 supersymmetry down to N=2, but respects the finiteness, and a light mass that, for simplicity, is set to zero. We find that coupling grows with the mass of the heavy intermediate states. Hence the latter do not decouple at low energies, leading to large logarithms that invalidate low-energy perturbation theory. Consequently, further manipulations are required to obtain a meaningful perturbative expansion. Enforcing decoupling through finite renormalizations, that absorb the heavy mass effects into a redefinition of the parameters of the lagrangian, introduces an arbitrary subtraction mass ..mu... The requirement that the S-matrix elements be independent of ..mu.. leads to a non-trivial renormalization-group equation for the low-energy theory, with a non-vanishing ..beta..-function.

Robust and efficient handling of yield surface discontinuities in elasto-plastic finite element calculations

DEFF Research Database (Denmark)

Clausen, Johan Christian; Damkilde, Lars; Andersen, Lars Vabbersgaard

2015-01-01

Purpose – The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in multisingular constitutive matrices which can cause numerical problems in elasto-plastic finite element...... documented in the literature all present “easy” calculation examples, e.g. low friction angles and few elements. The amendments presented in this paper result in robust elasto-plastic computations, making the solution of “hard” problems possible without introducing approximations in the yield surfaces...... calculations. These problems, however, are not documented in previous literature. In this paper an amendment to the Koiter formulation of the constitutive matrices for stress points located on discontinuities is proposed. Design/methodology/approach – First, a review of existing methods of handling yield...

The renormalization group and lattice QCD

International Nuclear Information System (INIS)

Gupta, R.

1989-01-01

This report discusses the following topics: scaling of thermodynamic quantities and critical exponents; scaling relations; block spin idea of Kadanoff; exact RG solution of the 1-d Ising model; Wilson's formulation of the renormalization group; linearized transformation matrix and classification of exponents; derivation of exponents from the eigenvalues of Τ αβ ; simple field theory: the gaussian model; linear renormalization group transformations; numerical methods: MCRG; block transformations for 4-d SU(N) LGT; asymptotic freedom makes QCD simple; non-perturbative β-function and scaling; and the holy grail: the renormalized trajectory

Renormalization methods in solid state physics

Energy Technology Data Exchange (ETDEWEB)

Nozieres, P [Institut Max von Laue - Paul Langevin, 38 - Grenoble (France)

1976-01-01

Renormalization methods in various solid state problems (e.g., the Kondo effect) are analyzed from a qualitative vantage point. Our goal is to show how the renormalization procedure works, and to uncover a few simple general ideas (universality, phenomenological descriptions, etc...).

The adjoint string at finite temperature

International Nuclear Information System (INIS)

Damgaard, P.H.

1986-10-01

Expectations for the behavior of the adjoint string at finite temperature are presented. In the Migdal-Kadanoff approximation a real-space renormalization group study of the effective Polyakov like action predicts a deconfinement-like crossover for adjoint sources at a temperature slightly below the deconfinement temperature of fundamental sources. This prediction is compared with a Monte Carlo simulation of SU(2) lattice gauge theory on an 8 3 x2 lattice. (orig.)

Regularization and renormalization of quantum field theory in curved space-time

International Nuclear Information System (INIS)

Bernard, C.; Duncan, A.

1977-01-01

It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli-Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by starting always from a manifestly generally covariant action, and the technical limitations of the dimensional reqularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions--it is shown that the trace anomaly previously found in dimensional regularization and some point-separation calculations also arises in perturbation theory when the theory is Pauli-Villars regulated. One then studies a specific solvable two-dimensional model of a massive scalar field in a Robertson-Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well defined finite expectation value for the stress-energy tensor. The particle production (less than 0 in/vertical bar/theta/sup mu nu/(x,t)/vertical bar/0 in greater than for t → + infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptotic regions t→ +- infinity independently of any weak field approximation. The extension of the model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed

Perturbative and constructive renormalization

International Nuclear Information System (INIS)

Veiga, P.A. Faria da

2000-01-01

These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)

Critical phenomena and renormalization group transformations

International Nuclear Information System (INIS)

Castellani, C.; Castro, C. di

1980-01-01

Our main goal is to guide the reader to find out the common rational behind the various renormalization procedures which have been proposed in the last ten years. In the first part of these lectures old arguments on universality and scaling will be briefly recalled. To our opinion these introductory remarks allow one to stress the physical origin of the two majore renormalization procedures, which have been used in the theory of critical phenomena: the Wilson and the field theoretic approach. All the general properties of a ''good'' renormalization transformation will also come out quite naturally. (author)

A low-energy β-function in a finite super-Yang-Mills model with multiple mass scales

International Nuclear Information System (INIS)

Foda, O.; Helayel-Neto, J.A.

1985-01-01

We compute the one-loop contribution to the low-energy light-fermion gauge coupling in a finite supersymmetric gauge theory with two mass scales: a heavy mass that breaks an initial N=4 supersymmetry down to N=2, but respects the finiteness, and a light mass that, for simplicity, is set to zero. We find that coupling grows with the mass of the heavy intermediate states. Hence the latter do not decouple at low energies, leading to large logarithms that invalidate low-energy perturbation theory. Consequently, further manipulations are required to obtain a meaningful perturbative expansion. Enforcing decoupling through finite renormalizations, that absorb the heavy mass effects into a redefinition of the parameters of the lagrangian, introduces an arbitrary subtraction mass μ. The requirement that the S-matrix elements be independent of μ leads to a non-trivial renormalization-group equation for the low-energy theory, with a non-vanishing β-function. (orig.)

A low-energy β-function in a finite super-Yang-Mills model with multiple mass scales

International Nuclear Information System (INIS)

Foda, O.; Helayel-Neto, J.A.

1984-08-01

We compute the one-loop contribution to the low-energy light-fermion gauge coupling in a finite supersymmetric gauge theory with two mass scales: a heavy mass that breaks an initial N=4 supersymmetry down to N=2, but respects the finiteness, and a light mass that, for simplicity, is set to zero. We find that the coupling grows with the mass of the heavy intermediate states. Hence the latter do not decouple at low energies, leading to large logarithms that invalidate low-energy perturbation theory. Consequently, further manipulations are required to obtain a meaningful perturbative expansion. Enforcing decoupling through finite renormalizations, that absorb the heavy mass effects into a redefinition of the parameters of the Lagrangian, introduces an arbitrary subtraction mass μ. The requirement that the S-matrix elements be independent of μ leads to a non-trivial renormalization-group equation for the low-energy theory, with a non-vanishing β-function. (author)

Ultracold atoms and the Functional Renormalization Group

International Nuclear Information System (INIS)

Boettcher, Igor; Pawlowski, Jan M.; Diehl, Sebastian

2012-01-01

We give a self-contained introduction to the physics of ultracold atoms using functional integral techniques. Based on a consideration of the relevant length scales, we derive the universal effective low energy Hamiltonian describing ultracold alkali atoms. We then introduce the concept of the effective action, which generalizes the classical action principle to full quantum status and provides an intuitive and versatile tool for practical calculations. This framework is applied to weakly interacting degenerate bosons and fermions in the spatial continuum. In particular, we discuss the related BEC and BCS quantum condensation mechanisms. We then turn to the BCS-BEC crossover, which interpolates between both phenomena, and which is realized experimentally in the vicinity of a Feshbach resonance. For its description, we introduce the Functional Renormalization Group approach. After a general discussion of the method in the cold atoms context, we present a detailed and pedagogical application to the crossover problem. This not only provides the physical mechanism underlying this phenomenon. More generally, it also reveals how the renormalization group can be used as a tool to capture physics at all scales, from few-body scattering on microscopic scales, through the finite temperature phase diagram governed by many-body length scales, up to critical phenomena dictating long distance physics at the phase transition. The presentation aims to equip students at the beginning PhD level with knowledge on key physical phenomena and flexible tools for their description, and should enable to embark upon practical calculations in this field.

The Background-Field Method and Noninvariant Renormalization

International Nuclear Information System (INIS)

Avdeev, L.V.; Kazakov, D.I.; Kalmykov, M.Yu.

1994-01-01

We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional σ model it is demonstrated that the background-field method gives incorrect results when the regularization (and/or renormalization) is noninvariant. In particular, it is found that the cut-off regularization and the differential renormalization belong to this class and are incompatible with the background-field method in theories with nonlinear symmetries. 17 refs

Perturbatively improving RI-MOM renormalization constants

Energy Technology Data Exchange (ETDEWEB)

Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-03-15

The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.

Renormalization as an extension problem on the Count our ordered formalism in FFTF

Energy Technology Data Exchange (ETDEWEB)

Franco, D.H.T. [Centro de Estudos de Fisica Teorica (CEFT), Belo Horizonte, MG (Brazil); Acebal, J.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas; Grupo de Fisica Teorica Jose Leite Lopes (GFT-JLL), Petropolis, RJ (Brazil)

2003-06-01

From a distributional-theoretical framework, we make efforts in order to fill a gap in the series of studies which discuss the inheritance of the renormalization behaviour of a finite temperature field theory (FTFT) from the analogous version in quantum field theory (QFT) at T=0. Renormalization is treated as a distributional extension problem having the mathematical structure disentangled as much as possible from the physical aspects. The purely technical details essential for the discussion are briefly reviewed in a handle manner for further theoretical physics applications. The analysis elucidates some qualitative and quantitative distinctions concerning the divergences in the perturbation series when it is considered the FTFT version associated to a given QFT. Despite the differences, it turns clear the reason why the leading ultraviolet behaviour keeps unaffected when it is considered the FTFT version associated to a given QFT. The study is model independent and the approach allows one to consider the FTFT both imaginary and real time formalism at once in a unified way in the contour ordered formalism. (author)

Golden mean Siegel disk universality and renormalization

OpenAIRE

Gaidashev, Denis; Yampolsky, Michael

2016-01-01

We provide a computer-assisted proof of one of the central open questions in one-dimensional renormalization theory -- universality of the golden-mean Siegel disks. We further show that for every function in the stable manifold of the golden-mean renormalization fixed point the boundary of the Siegel disk is a quasicircle which coincides with the closure of the critical orbit, and that the dynamics on the boundary of the Siegel disk is rigid. Furthermore, we extend the renormalization from on...

Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

Science.gov (United States)

Seiler, Christian; Evers, Ferdinand

2016-10-01

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

Spectral functions and transport coefficients from the functional renormalization group

Energy Technology Data Exchange (ETDEWEB)

Tripolt, Ralf-Arno

2015-06-03

In this thesis we present a new method to obtain real-time quantities like spectral functions and transport coefficients at finite temperature and density using the Functional Renormalization Group approach. Our non-perturbative method is thermodynamically consistent, symmetry preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations. We demonstrate the applicability of this method by calculating mesonic spectral functions as well as the shear viscosity for the quark-meson model. In particular, results are presented for the pion and sigma spectral function at finite temperature and chemical potential, with a focus on the regime near the critical endpoint in the phase diagram of the quark-meson model. Moreover, the different time-like and space-like processes, which give rise to a complex structure of the spectral functions, are discussed. Finally, based on the momentum dependence of the spectral functions, we calculate the shear viscosity and the shear viscosity to entropy density ratio using the corresponding Green-Kubo formula.

Differential renormalization of gauge theories

International Nuclear Information System (INIS)

Aguila, F. del; Perez-Victoria, M.

1998-01-01

The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author)

Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories

Energy Technology Data Exchange (ETDEWEB)

Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)

2013-08-01

In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).

Renormalization and plasma physics

Energy Technology Data Exchange (ETDEWEB)

Krommes, J.A.

1980-02-01

A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.

Renormalization and plasma physics

International Nuclear Information System (INIS)

Krommes, J.A.

1980-02-01

A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields

Dimensional regularization and renormalization of Coulomb gauge quantum electrodynamics

International Nuclear Information System (INIS)

Heckathorn, D.

1979-01-01

Quantum electrodynamics is renormalized in the Coulomb gauge with covariant counter terms and without momentum-dependent wave-function renormalization constants. It is shown how to dimensionally regularize non-covariant integrals occurring in this guage, and prove that the 'minimal' subtraction prescription excludes non-covariant counter terms. Motivated by the need for a renormalized Coulomb gauge formalism in certain practical calculations, the author introduces a convenient prescription with physical parameters. The renormalization group equations for the Coulomb gauge are derived. (Auth.)

G-Boson renormalizations and mixed symmetry states

International Nuclear Information System (INIS)

Scholten, O.

1986-01-01

In the IBA model the low-lying collective states are described in terms of a system of interacting s- and d-bosons. A boson can be interpreted as corresponding to collective J=0 or J=2 fermion pair states. As such the IBA model space can be seen as only a small subsector of the full shell model space. For medium heavy nuclei such a truncation of the model space is necessary to make calculations feasible. As is well known truncations of a model space make it necessary to renormalize the model parameters. In this work some renormalizations of the Hamiltonian and the E2 transition operator will be discussed. Special attention will be given to the implication of these renormalizations for the properties of mixed symmetry states. The effects of renormalization are obtained by considering the influence of fermion pair states that have been omitted from the model basis. Here the authors focus attention on the effect of the low-lying two particle J=4 state, referred to as g-boson or G-pair state. Renormalizations of the d-boson energy, the E2 effective charges, and symmetry force are discussed

Sigma models and renormalization of string loops

International Nuclear Information System (INIS)

Tseytlin, A.A.

1989-05-01

An extension of the ''σ-model β-functions - string equations of motion'' correspondence to the string loop level is discussed. Special emphasis is made on how the renormalization group acts in string loops and, in particular, on the renormalizability property of the generating functional Z-circumflex for string amplitudes (related to the σ model partition function integrated over moduli). Renormalization of Z-circumflex at one and two loop order is analyzed in some detail. We also discuss an approach to renormalization based on operators of insertion of topological fixtures. (author). 70 refs

Effective AdS/renormalized CFT

OpenAIRE

Fan, JiJi

2011-01-01

For an effective AdS theory, we present a simple prescription to compute the renormalization of its dual boundary field theory. In particular, we define anomalous dimension holographically as the dependence of the wave-function renormalization factor on the radial cutoff in the Poincare patch of AdS. With this definition, the anomalous dimensions of both single- and double- trace operators are calculated. Three different dualities are considered with the field theory being CFT, CFT with a dou...

Differential renormalization of gauge theories

Energy Technology Data Exchange (ETDEWEB)

Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)

1998-10-01

The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab

The two-loop renormalization of general quantum field theories

International Nuclear Information System (INIS)

Damme, R.M.J. van.

1984-01-01

This thesis provides a general method to compute all first order corrections to the renormalization group equations. This requires the computation of the first perturbative corrections to the renormalization group β-functions. These corrections are described by Feynman diagrams with two loops. The two-loop renormalization is treated for an arbitrary renormalization field theory. Two cases are considered: 1. the Yukawa sector; 2. the gauge coupling and the scalar potential. In a final section, the breakdown of unitarity in the dimensional reduction scheme is discussed. (Auth.)

Higher derivatives and renormalization in quantum cosmology

International Nuclear Information System (INIS)

Mazzitelli, F.D.

1991-10-01

In the framework of the canonical quantization of general relativity, quantum field theory on a fixed background formally arises in an expansion in powers of the Planck length. In order to renormalize the theory, quadratic terms in the curvature must be included in the gravitational action from the beginning. These terms contain higher derivatives which change the Hamiltonian structure of the theory completely, making the relation between the renormalized-theory and the original one not clear. We show that it is possible to avoid this problem. We replace the higher derivative theory by a second order one. The classical solutions of the latter are also solutions of the former. We quantize the theory, renormalize the infinities and show that there is a smooth limit between the classical and the renormalized theories. We work in a Robertson Walker minisuperspace with a quantum scalar field. (author). 32 refs

Eliminating infinities in the λφ4 theory by simple scaling

International Nuclear Information System (INIS)

Aragao, Cristiane M.L. de; Carneiro, C.E.I.

2006-01-01

We present an alternative method to remove infinities in the perturbative φ 4 theory. In our method, the renormalization is performed in two stages. Firstly, the infinities are eliminated by rescaling the Lagrangian. The Green functions obtained from this rescaled Lagrangian are finite to all orders in perturbation. Secondly, we fix the values of parameters of the resulting finite theory at a certain mass scale by using the standard renormalization conditions. This second stage allows us to derive renormalization equations which yields the critical behavior of the theory. We show that our method does not change the critical behavior of the λφ 4 theory in 4-ε dimensions. In particular, we recover the usual critical exponents

Finite Range Decomposition of Gaussian Processes

CERN Document Server

Brydges, C D; Mitter, P K

2003-01-01

Let $D$ be the finite difference Laplacian associated to the lattice $bZ^{d}$. For dimension $dge 3$, $age 0$ and $L$ a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent $G^{a}:=(a-D)^{-1}$ can be decomposed as an infinite sum of positive semi-definite functions $ V_{n} $ of finite range, $ V_{n} (x-y) = 0$ for $|x-y|ge O(L)^{n}$. Equivalently, the Gaussian process on the lattice with covariance $G^{a}$ admits a decomposition into independent Gaussian processes with finite range covariances. For $a=0$, $ V_{n} $ has a limiting scaling form $L^{-n(d-2)}Gamma_{ c,ast }{bigl (frac{x-y}{ L^{n}}bigr )}$ as $nrightarrow infty$. As a corollary, such decompositions also exist for fractional powers $(-D)^{-alpha/2}$, $0renormalization group on the lattice.

Fermionic functional integrals and the renormalization group

CERN Document Server

Feldman, Joel; Trubowitz, Eugene

2002-01-01

This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...

Renormalization group in statistical physics - momentum and real spaces

International Nuclear Information System (INIS)

Yukalov, V.I.

1988-01-01

Two variants of the renormalization group approach in statistical physics are considered, the renormalization group in the momentum and the renormalization group in the real spaces. Common properties of these methods and their differences are cleared up. A simple model for investigating the crossover between different universality classes is suggested. 27 refs

Renormalization in general theories with inter-generation mixing

International Nuclear Information System (INIS)

Kniehl, Bernd A.; Sirlin, Alberto

2011-11-01

We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with inter-generation mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of inter-generation mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from Matrix Algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties. (orig.)

On the renormalization group equations of quantum electrodynamics

International Nuclear Information System (INIS)

Hirayama, Minoru

1980-01-01

The renormalization group equations of quantum electrodynamics are discussed. The solution of the Gell-Mann-Low equation is presented in a convenient form. The interrelation between the Nishijima-Tomozawa equation and the Gell-Mann-Low equation is clarified. The reciprocal effective charge, so to speak, turns out to play an important role to discuss renormalization group equations. Arguments are given that the reciprocal effective charge vanishes as the renormalization momentum tends to infinity. (author)

Renormalization: infinity in today microscopic physics

International Nuclear Information System (INIS)

Zinn-Justin, J.

2000-01-01

The expectations put in quantum electrodynamics were deceived when first calculations showed that divergencies, due to the pinpoint aspect of the electron, continued to exist. Later, as a consequence of new experimental data and theoretical progress, an empirical method called renormalization was proposed to allow the evaluation of expressions involving infinite terms. The development of this method opened the way to the theory of re-normalizing fields and gave so successful results that it was applied to all fundamental interactions except gravity. This theory allowed the standard model in weak, electromagnetic and strong interactions to be confronted successfully with experimental data during more than 25 years. This article presents the progressive evolution of ideas in the concept of renormalization. (A.C.)

Renormalized modes in cuprate superconductors

Science.gov (United States)

Gupta, Anushri; Kumari, Anita; Verma, Sanjeev K.; Indu, B. D.

2018-04-01

The renormalized mode frequencies are obtained with the help of quantum dynamical approach of many body phonon Green's function technique via a general Hamiltonian (excluding BCS Hamiltonian) including the effects of phonons and electrons, anharmonicities and electron-phonon interactions. The numerical estimates have been carried out to study the renormalized mode frequency of high temperature cuprate superconductor (HTS) YBa2Cu3O7-δ using modified Born-Mayer-Huggins interaction potential (MBMHP) best applicable to study the dynamical properties of all HTS.

Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence

Science.gov (United States)

Rubinstein, Robert

1994-01-01

Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.

Renormalized thermodynamic entropy of black holes in higher dimensions

International Nuclear Information System (INIS)

Kim, S.P.; Kim, S.K.; Soh, K.; Yee, J.H.

1997-01-01

We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstroem black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon. copyright 1997 The American Physical Society

Renormalization group in modern physics

International Nuclear Information System (INIS)

Shirkov, D.V.

1988-01-01

Renormalization groups used in diverse fields of theoretical physics are considered. The discussion is based upon functional formulation of group transformations. This attitude enables development of a general method by using the notion of functional self-similarity which generalizes the usual self-similarity connected with power similarity laws. From this point of view the authors present a simple derivation of the renorm-group (RG) in QFT liberated from ultra-violet divergences philosophy, discuss the RG approach in other fields of physics and compare different RG's

On the modification of the Efimov spectrum in a finite cubic box

International Nuclear Information System (INIS)

Kreuzer, S.; Hammer, H.W.

2010-01-01

Three particles with large scattering length display a universal spectrum of three-body bound states called ''Efimov trimers''. We calculate the modification of the Efimov trimers of three identical bosons in a finite cubic box and compute the dependence of their energies on the box size using effective field theory. Previous calculations for positive scattering length that were perturbative in the finite-volume energy shift are extended to arbitrarily large shifts and negative scattering lengths. The renormalization of the effective field theory in the finite volume is explicitly verified. We investigate the effects of partial-wave mixing and study the behavior of shallow trimers near the dimer energy. Moreover, we provide numerical evidence for universal scaling of the finite-volume corrections. (orig.)

Optimization of renormalization group transformations in lattice gauge theory

International Nuclear Information System (INIS)

Lang, C.B.; Salmhofer, M.

1988-01-01

We discuss the dependence of the renormalization group flow on the choice of the renormalization group transformation (RGT). An optimal choice of the transformation's parameters should lead to a renormalized trajectory close to a few-parameter action. We apply a recently developed method to determine an optimal RGT to SU(2) lattice gauge theory and discuss the achieved improvement. (orig.)

Two-loop renormalization in the standard model, part I. Prolegomena

Energy Technology Data Exchange (ETDEWEB)

Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)

2006-12-15

In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)

Renormalization group analysis of a simple hierarchical fermion model

International Nuclear Information System (INIS)

Dorlas, T.C.

1991-01-01

A simple hierarchical fermion model is constructed which gives rise to an exact renormalization transformation in a 2-dimensional parameter space. The behaviour of this transformation is studied. It has two hyperbolic fixed points for which the existence of a global critical line is proven. The asymptotic behaviour of the transformation is used to prove the existence of the thermodynamic limit in a certain domain in parameter space. Also the existence of a continuum limit for these theories is investigated using information about the asymptotic renormalization behaviour. It turns out that the 'trivial' fixed point gives rise to a two-parameter family of continuum limits corresponding to that part of parameter space where the renormalization trajectories originate at this fixed point. Although the model is not very realistic it serves as a simple example of the appliclation of the renormalization group to proving the existence of the thermodynamic limit and the continuum limit of lattice models. Moreover, it illustrates possible complications that can arise in global renormalization group behaviour, and that might also be present in other models where no global analysis of the renormalization transformation has yet been achieved. (orig.)

Thermal geometry from CFT at finite temperature

Directory of Open Access Journals (Sweden)

Wen-Cong Gan

2016-09-01

Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

Thermal geometry from CFT at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Gan, Wen-Cong, E-mail: ganwencong@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Shu, Fu-Wen, E-mail: shufuwen@ncu.edu.cn [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Wu, Meng-He, E-mail: menghewu.physik@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China)

2016-09-10

We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

Renormalization of g-boson effects under weak coupling condition

International Nuclear Information System (INIS)

Zhang Zhanjun; Yang Jie; Liu Yong; Sang Jianping

1998-01-01

An approach based on perturbation theory is proposed to renormalized g-boson effects for sdgIBM system, which modifies that presented earlier by Druce et al. The weak coupling condition as the usage premise of the two approaches is proved to be satisfied. Two renormalization spectra are calculated for comparison and analyses. Results show that the g-boson effects are renormalized more completely by the approach proposed

Renormalization group theory of critical phenomena

International Nuclear Information System (INIS)

Menon, S.V.G.

1995-01-01

Renormalization group theory is a framework for describing those phenomena that involve a multitude of scales of variations of microscopic quantities. Systems in the vicinity of continuous phase transitions have spatial correlations at all length scales. The renormalization group theory and the pertinent background material are introduced and applied to some important problems in this monograph. The monograph begins with a historical survey of thermal phase transitions. The background material leading to the renormalization group theory is covered in the first three chapters. Then, the basic techniques of the theory are introduced and applied to magnetic critical phenomena in the next four chapters. The momentum space approach as well as the real space techniques are, thus, discussed in detail. Finally, brief outlines of applications of the theory to some of the related areas are presented in the last chapter. (author)

Renormalization and factorization scale analysis of b-barb production in antiproton-proton collisions

International Nuclear Information System (INIS)

Chyla, Jiri

2003-01-01

There is a sizable and systematic discrepancy between experimental data on the b-barb production in , p-barp, γp and γγ collisions and existing theoretical calculations within perturbative QCD. Before interpreting this discrepancy as a signal of new physics, it is important to understand quantitatively the ambiguities of conventional calculations. In this paper the uncertainty coming from renormalization and factorization scale dependence of finite order perturbation calculations of the total cross section of b-barb production in p-barp collisions is discussed in detail. It is shown that the mentioned discrepancy is reduced significantly if these scales are fixed via the Principle of Minimal Sensitivity. (author)

Renormalization techniques applied to the study of density of states in disordered systems

International Nuclear Information System (INIS)

Ramirez Ibanez, J.

1985-01-01

A general scheme for real space renormalization of formal scattering theory is presented and applied to the calculation of density of states (DOS) in some finite width systems. This technique is extended in a self-consistent way, to the treatment of disordered and partially ordered chains. Numerical results of moments and DOS are presented in comparison with previous calculations. In addition, a self-consistent theory for the magnetic order problem in a Hubbard chain is derived and a parametric transition is observed. Properties of localization of the electronic states in disordered chains are studied through various decimation averaging techniques and using numerical simulations. (author) [pt

Zeta Functions, Renormalization Group Equations, and the Effective Action

International Nuclear Information System (INIS)

Hochberg, D.; Perez-Mercader, J.; Molina-Paris, C.; Visser, M.

1998-01-01

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley-DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action and use this to derive the leading logarithms in the one-loop effective action for arbitrary quantum field theories. copyright 1998 The American Physical Society

Renormalization group approach in the turbulence theory

International Nuclear Information System (INIS)

Adzhemyan, L.Ts.; Vasil'ev, A.N.; Pis'mak, Yu.M.

1983-01-01

In the framework of the renormalization groUp approach in the turbulence theory sUggested in another paper, the problem of renormalization and evaluation of critical dimensions of composite operators is discussed. Renormalization of a system of operators of canonical dimension equal to 4, including the operator F=phiΔphi (where phi is the velocity field), is considered. It is shown that the critical dimension Δsub(F)=0. The appendice includes the brief proofs of two theorems: 1) the theorem on the equivalence between the arbitrary stochastic problem and quantum field theory; 2) the theorem which determines the reduction of Green functions of the stochastic problem to the hypersurface of coinciding times

Non-perturbative renormalization of three-quark operators

Energy Technology Data Exchange (ETDEWEB)

Goeckeler, Meinulf [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, Roger [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Kaltenbrunner, Thomas [Regensburg Univ. (DE). Inst. fuer Theoretische Physik] (and others)

2008-10-15

High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MS scheme at {mu}=2 GeV. (orig.)

Nonequilibrium Kondo effect by the equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias

Science.gov (United States)

Fang, Tie-Feng; Guo, Ai-Min; Sun, Qing-Feng

2018-06-01

We investigate Kondo correlations in a quantum dot with normal and superconducting electrodes, where a spin bias voltage is applied across the device and the local interaction U is either attractive or repulsive. When the spin current is blockaded in the large-gap regime, this nonequilibrium strongly correlated problem maps into an equilibrium model solvable by the numerical renormalization group method. The Kondo spectra with characteristic splitting due to the nonequilibrium spin accumulation are thus obtained at high precision. It is shown that while the bias-induced decoherence of the spin Kondo effect is partially compensated by the superconductivity, the charge Kondo effect is enhanced out of equilibrium and undergoes an additional splitting by the superconducting proximity effect, yielding four Kondo peaks in the local spectral density. In the charge Kondo regime, we find a universal scaling of charge conductance in this hybrid device under different spin biases. The universal conductance as a function of the coupling to the superconducting lead is peaked at and hence directly measures the Kondo temperature. Our results are of direct relevance to recent experiments realizing a negative-U charge Kondo effect in hybrid oxide quantum dots [Nat. Commun. 8, 395 (2017), 10.1038/s41467-017-00495-7].

Finite volume form factors in the presence of integrable defects

International Nuclear Information System (INIS)

Bajnok, Z.; Buccheri, F.; Hollo, L.; Konczer, J.; Takacs, G.

2014-01-01

We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate all polynomial corrections in the inverse of the volume. We tested our results, in the defect Lee–Yang model, against numerical data obtained by truncated conformal space approach (TCSA), which we improved by renormalization group methods adopted to the defect case. To perform these checks we determined the infinite volume defect form factors in the Lee–Yang model exactly, including their vacuum expectation values. We used these data to calculate the two point functions, which we compared, at short distance, to defect CFT. We also derived explicit expressions for the exact finite volume one point functions, which we checked numerically. In all of these comparisons excellent agreement was found

Renormalization group and fixed points in quantum field theory

International Nuclear Information System (INIS)

Hollowood, Timothy J.

2013-01-01

This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.

Simple renormalization group method for calculating geometrical and other equations of states

International Nuclear Information System (INIS)

Tsallis, C.; Schwaccheim, G.; Coniglio, A.

1984-01-01

A real space renormalization group procedure to calculate geometrical and thermal equations of states for the entire range of values of the external parameters is described. Its use is as simple as a Mean Field Approximation; however, it yields non trivial results and can be systematically improved. Such a procedure is illustrated by calculating, for all bond concentrations, the site mass density for the complete and the backbone percolating infinite clusters in square lattice: the results are quite satisfactory. (Author) [pt

Renormalizing Entanglement Distillation

Science.gov (United States)

Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T.; Eisert, Jens

2016-01-01

Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics—ideas from renormalization and matrix-product states and operators—with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.

Renormalization and 3-manifolds which fiber over the circle (AM-142)

CERN Document Server

McMullen, Curtis T

2014-01-01

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitativ

Phases of renormalized lattice gauge theories with fermions

International Nuclear Information System (INIS)

Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)

1979-01-01

Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory

Results in finite temperature quantum electrodynamics

International Nuclear Information System (INIS)

Down, D.M.

1985-01-01

First, three quantities of physical interest are calculated. The first two quantities are the self energy of the electron at order α and the self mass of the electron at order α 2 due to its interaction with a thermal bath of photons. The third quantity of physical interest is the thermal contribution to the self mass of the axion. Second, some formal developments are presented. First among these is the proof of an extension to the familiar optical theorem to cover processes taking place at finite temperature. Then an example of the application of the theorem is given for a simple field theory involving two types of scalar particles. The example illustrates that the relationship between the forward scattering amplitude and the total cross section is more complex at finite temperature than at zero temperature. Third, a method for calculating the wave function renormalization constant at finite temperature for an electron in a thermal bath of photons is presented. This method is compared with methods invented by other authors

Renormalization of the γ-ray strength functions of light nuclei

International Nuclear Information System (INIS)

Canbula, B.; Ersan, S.; Babacan, H.

2015-01-01

γ-ray strength function is the key input for the photonuclear reactions, which have a special astrophysical importance, and should be renormalized by using the nuclear level density for calculating the theoretical average radiative capture width, but performing such renormalization is challenging for light nuclei. With this motivation, recently introduced level density parameter formula including collective effects is used to calculate the average radiative capture width of light nuclei, and therefore to renormalize their γ-ray strength functions. Obtained normalization factors are tested in (n, γ) reactions for the necessity of renormalization for light nuclei. (author)

Unique determination of the effective potential in terms of renormalization group functions

International Nuclear Information System (INIS)

Chishtie, F. A.; Hanif, T.; McKeon, D. G. C.; Steele, T. G.

2008-01-01

The perturbative effective potential V in the massless λφ 4 model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition (d 4 V/dφ 4 )| φ=μ =λ is used, where μ represents the renormalization scale. Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal-subtraction (MS) renormalization group functions. Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V. An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme. As an example, the explicit five-loop effective potential is obtained from the known five-loop MS renormalization group functions and we explicitly sum the leading-logarithm, next-to-leading-logarithm, and further subleading-logarithm contributions to V. Extensions of these results to massless scalar QED are also presented. Because massless scalar QED has two couplings, conversion of the renormalization group functions from the MS scheme to the Coleman-Weinberg scheme requires the use of multiscale renormalization group methods.

Stationary spectra of short-wave convective and magnetostatic fluctuations in a finite-pressure plasma and anomalous heat conductivity

International Nuclear Information System (INIS)

Vakulenko, M.O.

1992-01-01

Within the general renormalized statistical approach, the low-frequency short-wave stationary spectra of potential and magnetic perturbations in a finite-pressure plasma, are obtained. Anomalous heat conductivity considerably enhances due to non-linear interaction between magnetic excitations. 11 refs. (author)

Investigation of renormalization effects in high temperature cuprate superconductors

International Nuclear Information System (INIS)

Zabolotnyy, Volodymyr B.

2008-01-01

It has been found that the self-energy of high-T C cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi 2 Sr 2 CaCu 2 O 8+δ and YBa 2 Cu 3 O 7-δ were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T C suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)

Renormalization in the complete Mellin representation of Feynman amplitudes

International Nuclear Information System (INIS)

Calan, C. de; David, F.; Rivasseau, V.

1981-01-01

The Feynmann amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM intergrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched. (orig.)

Renormalization in p-adic quantum field theory

International Nuclear Information System (INIS)

Smirnov, V.A.

1990-01-01

A version of p-adic perturbative Euclidean quantum field theory is presented. It is based on the new type of propagator which happens to be rather natural for p-adic space-time. Low-order Feynamn diagrams are explicity calculated and typical renormalization schemes are introduced: analytic, dimensional and BPHZ renormalizations. The calculations show that in p-adic Feynman integrals only logarithmic divergences appear. 14 refs.; 1 fig

Quantum field theory and phase transitions: universality and renormalization group

International Nuclear Information System (INIS)

Zinn-Justin, J.

2003-08-01

In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)

Wetting transitions: A functional renormalization-group approach

International Nuclear Information System (INIS)

Fisher, D.S.; Huse, D.A.

1985-01-01

A linear functional renormalization group is introduced as a framework in which to treat various wetting transitions of films on substrates. A unified treatment of the wetting transition in three dimensions with short-range interactions is given. The results of Brezin, Halperin, and Leibler in their three different regimes are reproduced along with new results on the multicritical behavior connecting the various regimes. In addition, the critical behavior as the coexistence curve is approached at complete wetting is analyzed. Wetting in the presence of long-range substrate-film interactions that fall off as power laws is also studied. The possible effects of the nonlinear terms in the renormalization group are examined briefly and it appears that they do not alter the critical behavior found using the truncated linear renormalization group

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models

Science.gov (United States)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Investigation of renormalization effects in high temperature cuprate superconductors

Energy Technology Data Exchange (ETDEWEB)

Zabolotnyy, Volodymyr B.

2008-04-16

It has been found that the self-energy of high-T{sub C} cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} and YBa{sub 2}Cu{sub 3}O{sub 7-{delta}} were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T{sub C} suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

International Nuclear Information System (INIS)

Defenu, N.; Mati, P.; Márián, I.G.; Nándori, I.; Trombettoni, A.

2015-01-01

We study the occurrence of spontaneous symmetry breaking (SSB) for O(N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N=1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions.

Renormalization using the background-field method

International Nuclear Information System (INIS)

Ichinose, S.; Omote, M.

1982-01-01

Renormalization using the background-field method is examined in detail. The subtraction mechanism of subdivergences is described with reference to multi-loop diagrams and one- and two-loop counter-term formulae are explicitly given. The original one-loop counter-term formula of 't Hooft is thereby improved. The present method of renormalization is far easier to manage than the usual one owing to the fact only gauge-invariant quantities are to be considered when worked in an appropriate gauge. Gravity and Yang-Mills theories are studied as examples. (orig.)

Field renormalization in photonic crystal waveguides

DEFF Research Database (Denmark)

Colman, Pierre

2015-01-01

A novel strategy is introduced in order to include variations of the nonlinearity in the nonlinear Schro¨dinger equation. This technique, which relies on renormalization, is in particular well adapted to nanostructured optical systems where the nonlinearity exhibits large variations up to two...... orders of magnitude larger than in bulk material. We show that it takes into account in a simple and efficient way the specificity of the nonlinearity in nanostructures that is determined by geometrical parameters like the effective mode area and the group index. The renormalization of the nonlinear...

Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD

CERN Document Server

Guagnelli, M; Peña, C; Sint, S; Vladikas, A

2006-01-01

We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\\Delta F = 1$ and $\\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.

Renormalization Methods - A Guide For Beginners

International Nuclear Information System (INIS)

Cardy, J

2004-01-01

The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard φ 4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

Energy Technology Data Exchange (ETDEWEB)

Elizalde, Emilio; Odintsov, Sergei D. [Instituto de Ciencias del Espacio (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Campus UAB, Carrer de Can Magrans, s/n, Cerdanyola del Vallès, Barcelona, 08193 Spain (Spain); Pozdeeva, Ekaterina O.; Vernov, Sergey Yu., E-mail: elizalde@ieec.uab.es, E-mail: odintsov@ieec.uab.es, E-mail: pozdeeva@www-hep.sinp.msu.ru, E-mail: svernov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 (Russian Federation)

2016-02-01

The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, n{sub s} and r, are close to the corresponding ones in the R{sup 2} and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.

On renormalization-invariant masses

International Nuclear Information System (INIS)

Fleming, H.; Furuya, K.

1978-02-01

It is shown that spontaneous generation of renormalization invariant mass is possible in infra-red stable theories with more than one coupling constant. If relations among the coupling constants are permitted the effect can be made compatible with pertubation theory

Evolution of topological features in finite antiferromagnetic Heisenberg chains

International Nuclear Information System (INIS)

Chen Changfeng

2003-01-01

We examine the behavior of nonlocal topological order in finite antiferromagnetic Heisenberg chains using the density matrix renormalization group techniques. We find that chains with even and odd site parity show very different behavior in the topological string order parameter, reflecting interesting interplay of the intrinsic magnetic correlation and the topological term in the chains. Analysis of the calculated string order parameter as a function of the chain length and the topological angle indicates that S=1/2 and S=1 chains show special behavior while all S>1 chains have similar topological structure. This result supports an earlier conjecture on the classification of quantum spin chains based on an analysis of their phase diagrams. Implications of the topological behavior in finite quantum spin chains are discussed

Gauge-independent renormalization of the N2HDM

Science.gov (United States)

Krause, Marcel; López-Val, David; Mühlleitner, Margarete; Santos, Rui

2017-12-01

The Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) is an interesting benchmark model for a Higgs sector consisting of two complex doublet and one real singlet fields. Like the Next-to-Minimal Supersymmetric extension (NMSSM) it features light Higgs bosons that could have escaped discovery due to their singlet admixture. Thereby, the model allows for various different Higgs-to-Higgs decay modes. Contrary to the NMSSM, however, the model is not subject to supersymmetric relations restraining its allowed parameter space and its phenomenology. For the correct determination of the allowed parameter space, the correct interpretation of the LHC Higgs data and the possible distinction of beyond-the-Standard Model Higgs sectors higher order corrections to the Higgs boson observables are crucial. This requires not only their computation but also the development of a suitable renormalization scheme. In this paper we have worked out the renormalization of the complete N2HDM and provide a scheme for the gauge-independent renormalization of the mixing angles. We discuss the renormalization of the Z_2 soft breaking parameter m 12 2 and the singlet vacuum expectation value v S . Both enter the Higgs self-couplings relevant for Higgs-to-Higgs decays. We apply our renormalization scheme to different sample processes such as Higgs decays into Z bosons and decays into a lighter Higgs pair. Our results show that the corrections may be sizable and have to be taken into account for reliable predictions.

Relativistic time-dependent Fermion-mass renormalization using statistical regularization

Science.gov (United States)

Kutnink, Timothy; McMurray, Christian; Santrach, Amelia; Hockett, Sarah; Barcus, Scott; Petridis, Athanasios

2017-09-01

The time-dependent electromagnetically self-coupled Dirac equation is solved numerically by means of the staggered-leap-frog algorithm with reflecting boundary conditions. The stability region of the method versus the interaction strength and the spatial-grid size over time-step ratio is established. The expectation values of several dynamic operators are then evaluated as functions of time. These include the fermion and electromagnetic energies and the fermion dynamic mass. There is a characteristic, non-exponential, oscillatory dependence leading to asymptotic constants of these expectation values. In the case of the fermion mass this amounts to renormalization. The dependence of the expectation values on the spatial-grid size is evaluated in detail. Furthermore, the contribution of positive and negative energy states to the asymptotic values and the gauge fields is analyzed. Statistical regularization, employing a canonical ensemble whose temperature is the inverse of the grid size, is used to remove the grid-size and momentum-dependence and produce a finite result in the continuum limit.

Fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models

Energy Technology Data Exchange (ETDEWEB)

Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)

1983-04-28

We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

Transformation of renormalization groups in 2N-component fermion hierarchical model

International Nuclear Information System (INIS)

Stepanov, R.G.

2006-01-01

The 2N-component fermion model on the hierarchical lattice is studied. The explicit formulae for renormalization groups transformation in the space of coefficients setting the Grassmannian-significant density of the free measure are presented. The inverse transformation of the renormalization group is calculated. The definition of immovable points of renormalization groups is reduced to solving the set of algebraic equations. The interesting connection between renormalization group transformations in boson and fermion hierarchical models is found out. It is shown that one transformation is obtained from other one by the substitution of N on -N [ru

Renormalization of Hamiltonian QCD

International Nuclear Information System (INIS)

Andrasi, A.; Taylor, John C.

2009-01-01

We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

Cohomology and renormalization of BFYM theory in three dimensions

International Nuclear Information System (INIS)

Accardi, A.; Belli, A.; Zeni, M.

1997-01-01

The first-order formalism for the 3D Yang-Mills theory is considered and two different formulations are introduced, in which the gauge theory appears to be a deformation of the topological BF theory. We perform the quantization and the algebraic analysis of the renormalization of both the models, which are found to be anomaly free. We discuss also their stability against radiative corrections, giving the full structure of possible counterterms, requiring an involved matricial renormalization of fields and sources. Both models are then proved to be equivalent to the Yang-Mills theory at the renormalized level. (orig.)

Renormalization transformation of periodic and aperiodic lattices

International Nuclear Information System (INIS)

Macia, Enrique; Rodriguez-Oliveros, Rogelio

2006-01-01

In this work we introduce a similarity transformation acting on transfer matrices describing the propagation of elementary excitations through either periodic or Fibonacci lattices. The proposed transformation can act at two different scale lengths. At the atomic scale the transformation allows one to express the systems' global transfer matrix in terms of an equivalent on-site model one. Correlation effects among different hopping terms are described by a series of local phase factors in that case. When acting on larger scale lengths, corresponding to short segments of the original lattice, the similarity transformation can be properly regarded as describing an effective renormalization of the chain. The nature of the resulting renormalized lattice significantly depends on the kind of order (i.e., periodic or quasiperiodic) of the original lattice, expressing a delicate balance between chemical complexity and topological order as a consequence of the renormalization process

Anisotropic square lattice Potts ferromagnet: renormalization group treatment

International Nuclear Information System (INIS)

Oliveira, P.M.C. de; Tsallis, C.

1981-01-01

The choice of a convenient self-dual cell within a real space renormalization group framework enables a satisfactory treatment of the anisotropic square lattice q-state Potts ferromagnet criticality. The exact critical frontier and dimensionality crossover exponent PHI as well as the expected universality behaviour (renormalization flow sense) are recovered for any linear scaling factor b and all values of q(q - [pt

All-order renormalization of propagator matrix for fermionic system with flavor mixing

Energy Technology Data Exchange (ETDEWEB)

Kniehl, Bernd A. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics

2013-08-15

We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form.

Setting the renormalization scale in QCD: The principle of maximum conformality

DEFF Research Database (Denmark)

Brodsky, S. J.; Di Giustino, L.

2012-01-01

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormali......A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when...... the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta...... = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit...

Temperature dependent quasiparticle renormalization in nickel and iron

Energy Technology Data Exchange (ETDEWEB)

Ovsyannikov, Ruslan; Thirupathaiah, Setti; Sanchez-Barriga, Jaime; Fink, Joerg; Duerr, Hermann [Helmholtz Zentrum Berlin, BESSY II, Albert-Einstein-Strasse 15, D-12489 Berlin (Germany)

2010-07-01

One of the fundamental consequences of electron correlation effects is that the bare particles in solids become 'dressed' with an excitation cloud resulting in quasiparticles. Such a quasiparticle will carry the same spin and charge as the original particle, but will have a renormalized mass and a finite lifetime. The properties of many-body interactions are described with a complex function called self energy which is directly accessible to modern high-resolution angle resolved photoemission spectroscopy (ARPES). Ferromagnetic metals like nickel or iron offers the exciting possibility to study the spin dependence of quasiparticle coupling to bosonic modes. Utilizing the exchange split band structure as an intrinsic 'spin detector' it is possible to distinguish between electron-phonon and electron-magnon coupling phenomena. In this contribution we will report a systematic investigation of the k- and temperature dependence of the electron-boson coupling in nickel and iron metals as well as discuss origin of earlier observed anomalous lifetime broadening of majority spin states of nickel at Fermi level.

Multiscale unfolding of real networks by geometric renormalization

Science.gov (United States)

García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles

2018-06-01

Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.

Finite Unification: Theory, Models and Predictions

CERN Document Server

Heinemeyer, S; Zoupanos, G

2011-01-01

All-loop Finite Unified Theories (FUTs) are very interesting N=1 supersymmetric Grand Unified Theories (GUTs) realising an old field theory dream, and moreover have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensional couplings that guarantee the vanishing of all beta-functions in certain N=1 GUTs even to all orders. Furthermore developments in the soft supersymmetry breaking sector of N=1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory, too. Based on the above theoretical framework phenomenologically consistent FUTs have been constructed. Here we review FUT models based on the SU(5) and SU(3)^3 gauge groups and their predictions. Of particular interest is the Hig...

Setting the renormalization scale in pQCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

Energy Technology Data Exchange (ETDEWEB)

Ma, Hong -Hao [Chongqing Univ., Chongqing (People' s Republic of China); Wu, Xing -Gang [Chongqing Univ., Chongqing (People' s Republic of China); Ma, Yang [Chongqing Univ., Chongqing (People' s Republic of China); Brodsky, Stanley J. [Stanford Univ., Stanford, CA (United States); Mojaza, Matin [KTH Royal Inst. of Technology and Stockholm Univ., Stockholm (Sweden)

2015-05-26

A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R

Fisher's Zeros as the Boundary of Renormalization Group Flows in Complex Coupling Spaces

International Nuclear Information System (INIS)

Denbleyker, A.; Du Daping; Liu Yuzhi; Meurice, Y.; Zou Haiyuan

2010-01-01

We propose new methods to extend the renormalization group transformation to complex coupling spaces. We argue that Fisher's zeros are located at the boundary of the complex basin of attraction of infrared fixed points. We support this picture with numerical calculations at finite volume for two-dimensional O(N) models in the large-N limit and the hierarchical Ising model. We present numerical evidence that, as the volume increases, the Fisher's zeros of four-dimensional pure gauge SU(2) lattice gauge theory with a Wilson action stabilize at a distance larger than 0.15 from the real axis in the complex β=4/g 2 plane. We discuss the implications for proofs of confinement and searches for nontrivial infrared fixed points in models beyond the standard model.

Introduction to the nonequilibrium functional renormalization group

International Nuclear Information System (INIS)

Berges, J.; Mesterházy, D.

2012-01-01

In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences include the absence of a fluctuation-dissipation relation for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, where the corresponding scale-invariant system becomes independent of the details of the initial density matrix. We discuss some basic examples, for which we derive a hierarchy of fixed point solutions with increasing complexity from vacuum and thermal equilibrium to nonequilibrium. The latter solutions are then associated to the phenomenon of turbulence in quantum field theory.

Phase transition for a uniformly frustrated 19-vertex model by use of the density matrix renormalization group

International Nuclear Information System (INIS)

Honda, Yasushi; Horiguchi, Tsuyoshi

2001-01-01

We investigate a uniformly frustrated 19-vertex model with an anisotropy parameter η by use of the density matrix renormalization group for the transfer matrix for 0.6≤η≤1.3. The scaling dimension x is calculated from eigenvalues of the transfer matrix for several values η. The finite-size scaling analyses with a logarithmic correction are carried out in order to determine transition temperatures. It is found that there are two kinds of phase transitions, although there is a possibility of a single transition. This result is not compatible with the result for the uniformly frustrated XY model

Renormalization Group in different fields of theoretical physics

International Nuclear Information System (INIS)

Shirkov, D.V.

1992-02-01

A very simple and general approach to the symmetry that is widely known as a Renormalization Group symmetry is presented. It essentially uses a functional formulation of group transformations that can be considered as a generalization of self-similarity transformations well known in mathematical physics since last century. This generalized Functional Self-Similarity symmetry and corresponding group transformations are discussed first for a number of simple physical problems taken from diverse fields of classical physics as well as for QED. Then we formulate the Renorm-Group Method as a regular procedure that essentially improves the approximate solutions near the singularity. After that we discuss relations between different formulations of Renormalization Group as they appear in various parts of a modern theoretical physics. Finally we present several topics of RGM application in modern QFT. (author)

Hypercuboidal renormalization in spin foam quantum gravity

Science.gov (United States)

Bahr, Benjamin; Steinhaus, Sebastian

2017-06-01

In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.

Renormalization of a distorted gauge: invariant theory

International Nuclear Information System (INIS)

Hsu, J.P.; Underwood, J.A.

1976-02-01

A new type of renormalizable theory involving massive Yang-Mills fields whose mass is generated by an intrinsic breakdown of the usual local gauge symmetry is considered. However, the Lagrangian has a distorted gauge symmetry which leads to the Ward-Takahashi (W-T) identities. Also, the theory is independent of the gauge parameter xi. An explicit renormalization at the oneloop level is completely carried out by exhibiting counter terms, defining the physical parameters and computing all renormalization constants to check the W-T identities

Renormalization theory of stationary homogeneous strong turbulence in a collisionless plasma

International Nuclear Information System (INIS)

Zhang, Y.Z.

1984-01-01

A renormalization procedure for the perturbation expansion of the Vlasov-Poisson equation is presented to describe stationary homogeneous turbulence. By using the diagramatic scheme the theory is shown to be renormalizable to any order. The expressions for the renormalized propagator, the renormalized dielectric function, and the intrinsically incoherent source are given. The renormalization leads to a complete separation of the fluctuating distribution function f/sub k/ into two parts, the coherent part, which is proved to represent the dielectric effect of the medium, and the intrinsically incoherent part, which represents the effect of nonlinear source. The turbulent collisional operator in the transport equation is proved equal to GAMMA 0 , the frequency broadening when k = 0

Renormalization method and singularities in the theory of Langmuir turbulence

International Nuclear Information System (INIS)

Pelletier, G.

1977-01-01

The method of renormalization, using propagators and diagrams, is recalled with enough mathematical details to be read and used by a non-specialist. The Markovian models are discussed and applied to plasma turbulence. The physical meaning of the diagrams is exhibited. In addition to the usual resonance broadening, an improved renormalization is set out, including broadening of the nonlinear resonance with a beat wave by induced scattering. This improved renormalization is emphasized. In the case of Langmuir turbulence, it removes difficulties arising at the group velocity, and enhances large-scale induced-scattering diffusion. (author)

High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and n{sub f} = 4 Wilson fermions

Energy Technology Data Exchange (ETDEWEB)

Brambilla, M.; Di Renzo, F. [Universita di Parma (Italy); INFN, Gruppo Collegato di Parma, Dipartimento di Fisica e Scienze della Terra, Parma (Italy); Hasegawa, M. [Universita di Parma (Italy); Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation); INFN, Gruppo Collegato di Parma, Dipartimento di Fisica e Scienze della Terra, Parma (Italy)

2014-07-15

This is the third of a series of papers on three-loop computation of renormalization constants for Lattice QCD. Our main points of interest are results for the regularization defined by the Iwasaki gauge action and n{sub f} Wilson fermions. Our results for quark bilinears renormalized according to the RI'-MOM scheme can be compared to non-perturbative results. The latter are available for twisted mass QCD: being defined in the chiral limit, the renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of boosted perturbation theory and the disentanglement of irrelevant and finite-volume contributions. Discussing these issues we consider not only the new results of this paper, but also those for the regularization defined by the tree-level Symanzik improved gauge action and n{sub f} Wilson fermions, which we presented in a recent paper of ours. We finally comment on the extent to which the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI'-MOM scheme. (orig.)

Dimension 7 operators in the b{yields}s transition

Energy Technology Data Exchange (ETDEWEB)

Chalons, G. [Karlsruhe Univ. (T.H.) (Germany). Inst. fuer Theoretische Teilchenphysik; Domingo, F. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-03-15

We extend the low-energy effective field theory relevant for b{yields}s transitions up to operators of mass-dimension 7 and compute the associated anomalous-dimension matrix. We then compare our findings to the known results for dimension 6 operators and derive a solution for the renormalization group equations involving operators of dimension 7. We finally apply our analysis to a particularly simple case where the Standard Model is extended by an electroweak-magnetic operator and consider limits on this scenario from the decays B{sub s}{yields}{mu}{sup +}{mu}{sup -} and B{yields}K{nu} anti {nu}.

The fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models

International Nuclear Information System (INIS)

Foda, O.E.

1983-01-01

We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes. (orig.)

Simple perturbative renormalization scheme for supersymmetric gauge theories

Energy Technology Data Exchange (ETDEWEB)

Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)

1983-06-30

We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/..delta..)/sup -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.

Off-shell renormalization in Higgs effective field theories

Science.gov (United States)

Binosi, Daniele; Quadri, Andrea

2018-04-01

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential ˜ {({Φ}^{\\dagger}Φ -υ^2/2)}^N with N arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields X 1,2, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the N → ∞ case.

Some applications of renormalized RPA in bosonic field theories

International Nuclear Information System (INIS)

Hansen, H.; Chanfray, G.

2003-01-01

We present some applications of the renormalized RPA in bosonic field theories. We first present some developments for the explicit calculation of the total energy in Φ 4 theory and discuss its phase structure in 1 + 1 dimensions. We also demonstrate that the Goldstone theorem is satisfied in the O(N) model within the renormalized RPA. (authors)

The Physical Renormalization of Quantum Field Theories

International Nuclear Information System (INIS)

Binger, Michael William.; Stanford U., Phys. Dept.; SLAC

2007-01-01

The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, α(k 1 2 , k 2 2 , k 3 2 ), depends on three momentum scales and gives rise to an effective scale Q eff 2 (k 1 2 , k 2 2 , k 3 2 ) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green

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.)

Space-time versus world-sheet renormalization group equation in string theory

International Nuclear Information System (INIS)

Brustein, R.; Roland, K.

1991-05-01

We discuss the relation between space-time renormalization group equation for closed string field theory and world-sheet renormalization group equation for first-quantized strings. Restricting our attention to massless states we argue that there is a one-to-one correspondence between the fixed point solutions of the two renormalization group equations. In particular, we show how to extract the Fischler-Susskind mechanism from the string field theory equation in the case of the bosonic string. (orig.)

Renormalization scheme-invariant perturbation theory

International Nuclear Information System (INIS)

Dhar, A.

1983-01-01

A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables. (orig.)

Renormalization-group theory for the eddy viscosity in subgrid modeling

Science.gov (United States)

Zhou, YE; Vahala, George; Hossain, Murshed

1988-01-01

Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

Renormalization of gauge theories without cohomology

International Nuclear Information System (INIS)

Anselmi, Damiano

2013-01-01

We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

On truncations of the exact renormalization group

CERN Document Server

Morris, T R

1994-01-01

We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

Energy Technology Data Exchange (ETDEWEB)

Groh, Kai

2012-10-15

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

International Nuclear Information System (INIS)

Groh, Kai

2012-10-01

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of

Extended BPH renormalization of cutoff scalar field theories

International Nuclear Information System (INIS)

Chalmers, G.

1996-01-01

We show through the use of diagrammatic techniques and a newly adapted BPH renormalization method that general momentum cutoff scalar field theories in four dimensions are perturbatively renormalizable. Weinberg close-quote s convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. The naive use of the convergence theorem together with the BPH method is not appropriate for understanding the local divergences and renormalizability of these theories. We also show that the renormalized Green close-quote s functions are the same as in ordinary Φ 4 theory up to corrections suppressed by inverse powers of the cutoff. These conclusions are consistent with those of existing proofs based on the renormalization group. copyright 1996 The American Physical Society

Casimir effect at finite temperature for the Kalb-Ramond field

International Nuclear Information System (INIS)

Belich, H.; Silva, L. M.; Helayeel-Neto, J. A.; Santana, A. E.

2011-01-01

We use the thermofield dynamics formalism to obtain the energy-momentum tensor for the Kalb-Ramond field in a topology S 1 xS 1 xR 2 . The compactification is carried out by a generalized thermofield dynamics-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor. The expressions for the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and the results may be important for applications, as in cuprate superconductivity, for instance.

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.

Renormalization Scale-Fixing for Complex Scattering Amplitudes

Energy Technology Data Exchange (ETDEWEB)

Brodsky, Stanley J.; /SLAC; Llanes-Estrada, Felipe J.; /Madrid U.

2005-12-21

We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude which can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.

Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole.

Science.gov (United States)

Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten

2017-04-07

We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.

Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem

CERN Document Server

Gaydashev, D G

2006-01-01

The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this explanation, the hyperbolicity of renormalization, has not been proved yet. The present work considers a cylinder renormalization - a novel type of renormalization for holomorphic maps with a Siegel disk which is better suited for a hyperbolicity proof. A key element of a cylinder renormalization of a holomorphic map is a conformal isomorphism of a dynamical quotient of a subset of $\\field{C}$ to a bi-infinite cylinder $\\field{C} / \\field{Z}$. A construction of this conformal isomorphism is an implicit procedure which can be performed using the Measurable Riemann Mapping Theorem. We present a constructive proof of the Mea...

Renormalization group theory of phase transitions in square Ising systems

International Nuclear Information System (INIS)

Nienhuis, B.

1978-01-01

Some renormalization group calculations are presented on a number of phase transitions in a square Ising model, both second and first order. Of these transitions critical exponents are calculated, the amplitudes of the power law divergences and the locus of the transition. In some cases attention is paid to the thermodynamic functions also far from the critical point. Universality and scaling are discussed and the renormalization group theory is reviewed. It is shown how a renormalization transformation, which relates two similar systems with different macroscopic dimensions, can be constructed, and how some critical properties of the system follow from this transformation. Several numerical and analytical applications are presented. (Auth.)

Renormalization of the g-boson effects for Os isotopes

International Nuclear Information System (INIS)

Zhang Zhanjun; Liu Yong; Sang Jianping

1996-01-01

A modified renormalization approach based on that proposed by Druce et al. is presented. The overall agreement between the spectra calculated here and the accurate spectra is significantly improved. We also use Druce's approach to generate the renormalized spectra. It is shown that in our microscopic study, both of the approaches are very useful to the determination of several free parameters of fermion residual interactions

Renormalization Group Reduction of Non Integrable Hamiltonian Systems

International Nuclear Information System (INIS)

Tzenov, Stephan I.

2002-01-01

Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail

Poissonian renormalizations, exponentials, and power laws.

Science.gov (United States)

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Loop optimization for tensor network renormalization

Science.gov (United States)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

Structure of the vertex function in finite quantum electrodynamics

International Nuclear Information System (INIS)

Mannheim, P.D.

1975-01-01

We study the structure of the renormalized electromagnetic current vertes, GAMMA-tilde/sub μ/(p,p+q,q), in finite quantum electrodynamics. Using conformal invariance we find that GAMMA-tilde/sub μ/(p,p,0) takes the simple form of Z 1 γ/sub μ/ when the external fermions are far off the mass shell. We interpret this result as an old theorem on the structure of the vertex function due to Gell--Mann and Zachariasen. We give the general structure of the vertex for arbitrary momentum transfer parametrically, and discuss how the Bethe--Salpeter equation and the Federbush--Johnson theorem are satisfied. We contrast the meaning of pointlike in a finite field theory with the meaning understood in the parton model. We discuss to what extent the condition Z 1 = 0, which may hold in conformal theories other than finite quantum electrodynamics, may be interpreted as a bootstrap condition. We show that the vanishing of Z 1 prevents their being bound states in the Migdal--Polyakov bootstrap

Metastability of the (φiφi)32 model at finite temperature and density

International Nuclear Information System (INIS)

Ananos, G.N.J.; Malbouisson, A.P.C.; Svaiter, N.F.

1996-11-01

Using concurrently the dimensional and analytic regularization methods we applied the Gross-Neveu model at finite temperature and density (chemical potential) in a D-dimensional spacetime. The renormalized effective potential is presented at the one-loop approximation. In the case of non-zero chemical potential we show that the effective potential acquires an imaginary part, which means that the system becomes metastable, indicating the possibility of a first phase transition. (author)

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

KAUST Repository

Kumar, Manoranjan

2016-02-03

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N=3n+1≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB. The ground state (GS) and spin densities ρr=⟨Szr⟩ at site r are quite different for junctions with S=1/2, 1, 3/2, and 2. The GS has finite total spin SG=2S(S) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0(<0) at sites of the larger (smaller) sublattice. S=1/2 junctions have delocalized states and decreasing spin densities with increasing N. S=1 junctions have four localized Sz=1/2 states at the end of each arm and centered on the junction, consistent with localized states in S=1 chains with finite Haldane gap. The GS of S=3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S=1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S=3/2 or 2 junctions.

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

KAUST Repository

Kumar, Manoranjan; Parvej, Aslam; Thomas, Simil; Ramasesha, S.; Soos, Z. G.

2016-01-01

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N=3n+1≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB. The ground state (GS) and spin densities ρr=⟨Szr⟩ at site r are quite different for junctions with S=1/2, 1, 3/2, and 2. The GS has finite total spin SG=2S(S) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0(<0) at sites of the larger (smaller) sublattice. S=1/2 junctions have delocalized states and decreasing spin densities with increasing N. S=1 junctions have four localized Sz=1/2 states at the end of each arm and centered on the junction, consistent with localized states in S=1 chains with finite Haldane gap. The GS of S=3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S=1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S=3/2 or 2 junctions.

One-loop renormalization of a gravity-scalar system

Energy Technology Data Exchange (ETDEWEB)

Park, I.Y. [Philander Smith College, Department of Applied Mathematics, Little Rock, AR (United States)

2017-05-15

Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)

One-loop renormalization of a gravity-scalar system

International Nuclear Information System (INIS)

Park, I.Y.

2017-01-01

Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)

One-loop renormalization of a gravity-scalar system

Science.gov (United States)

Park, I. Y.

2017-05-01

Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the "mass" term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information.

The ab-initio density matrix renormalization group in practice

Energy Technology Data Exchange (ETDEWEB)

Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Nakatani, Naoki [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Catalysis Research Center, Hokkaido University, Kita 21 Nishi 10, Sapporo, Hokkaido 001-0021 (Japan)

2015-01-21

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

The ab-initio density matrix renormalization group in practice.

Science.gov (United States)

Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic

2015-01-21

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

Strong renormalization scheme dependence in τ-lepton decay: Fact or fiction?

International Nuclear Information System (INIS)

Chyla, J.

1995-01-01

The question of the renormalization scheme dependence of the τ semileptonic decay rate is examined in response to a recent criticism. Particular attention is payed to a distinction between a consistent quantitative description of this dependence and the actual selection of a subset of ''acceptable'' renormalization schemes. It is pointed out that this criticism is valid only within a particular definition of the ''strength'' of the renormalization scheme dependence and should not discourage further attempts to use the semileptonic τ decay rate for quantitative tests of perturbative QCD

A note on nonperturbative renormalization of effective field theory

Energy Technology Data Exchange (ETDEWEB)

Yang Jifeng [Department of Physics, East China Normal University, Shanghai 200062 (China)

2009-08-28

Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.

A note on nonperturbative renormalization of effective field theory

International Nuclear Information System (INIS)

Yang Jifeng

2009-01-01

Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.

Exact renormalization group for gauge theories

International Nuclear Information System (INIS)

Balaban, T.; Imbrie, J.; Jaffe, A.

1984-01-01

Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study

Supersymmetric QED at finite temperature and the principle of equivalence

International Nuclear Information System (INIS)

Robinett, R.W.

1985-01-01

Unbroken supersymmetric QED is examined at finite temperature and it is shown that the scalar and spinor members of a chiral superfield acquire different temperature-dependent inertial masses. By considering the renormalization of the energy-momentum tensor it is also shown that the T-dependent scalar-spinor gravitational masses are also no longer degenerate and, moreover, are different from their T-dependent inertial mass shifts implying a violation of the equivalence principle. The temperature-dependent corrections to the spinor (g-2) are also calculated and found not to vanish

Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian

Science.gov (United States)

Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.

2018-03-01

Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.

Application of 't Hooft's renormalization scheme to two-loop calculations 230

International Nuclear Information System (INIS)

Vladimirov, A.A.

1975-01-01

The advantages of the Hooft scheme for asymptotic calculations in the renormalization group have been demonstrated. Two-loop calculations have been carried out in three renormalized models: in scalar electrodynamics, in a pseudoscalar Yukawa theory and in the Weiss-Zumino supersymmetrical model [ru

Exact renormalization group equations: an introductory review

Science.gov (United States)

Bagnuls, C.; Bervillier, C.

2001-07-01

We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.

Noncommutative quantum field theory: attempts on renormalization

International Nuclear Information System (INIS)

Popp, L.

2002-05-01

Quantum field theory is the art of dealing with problems at small distances or, equivalently, large momenta. Although there are different approaches (string theory, for example), it is generally accepted that these principles cannot be extrapolated to arbitrarily small distances as can be shown by applying simple, heuristic arguments. Therefore, the concept of space-time as a differential manifold has to be replaced by something else at such scales, the road we have chosen to follow is noncommutative geometry. We start from the basic relation [ x μ , x ν ] = i θ { μν}, where θ is a (usually) constant, antisymmetric matrix. This relation amounts to a noncommutativity of position measurements, or, put differently, the points are somehow 'smeared' out, which should have a positive effect on field theory since infinities arise from point-like interactions. However, it was shown that the effects of the commutation relation (leading to the so-called Moyal product) do not necessarily cure the divergences but introduce a new kind of problem: whereas UV-divergent integrals are rendered finite by phase factors (that arise as a consequence of the Moyal product), this same kind of 'regularization' introduces IR-divergences which led to the name 'UV/IR-mixing' for this problem. In order to overcome this peculiarity, one expands the action in θ which is immediate for the phase factors but requires the so-called Seiberg-Witten map for the fields. In this thesis, we emphasize the derivation of the Seiberg-Witten map by using noncommutative Lorentz symmetries, which is more general than the original derivation. After that, we concentrate on a treatment of θ-expanded theories and their renormalization, where it can be shown that the photon self-energy of noncommutative Maxwell theory can be renormalized to all orders in hbar and θ when the freedom in the Seiberg-Witten map (there are ambiguities in the map) is exploited. Although this is very promising, it cannot be

Quantum renormalization group approach to quantum coherence and multipartite entanglement in an XXZ spin chain

Energy Technology Data Exchange (ETDEWEB)

Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: xujb@zju.edu.cn [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)

2017-01-30

We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.

Renormalization group theory of earthquakes

Directory of Open Access Journals (Sweden)

H. Saleur

1996-01-01

Full Text Available We study theoretically the physical origin of the proposed discrete scale invariance of earthquake processes, at the origin of the universal log-periodic corrections to scaling, recently discovered in regional seismic activity (Sornette and Sammis (1995. The discrete scaling symmetries which may be present at smaller scales are shown to be robust on a global scale with respect to disorder. Furthermore, a single complex exponent is sufficient in practice to capture the essential properties of the leading correction to scaling, whose real part may be renormalized by disorder, and thus be specific to the system. We then propose a new mechanism for discrete scale invariance, based on the interplay between dynamics and disorder. The existence of non-linear corrections to the renormalization group flow implies that an earthquake is not an isolated 'critical point', but is accompanied by an embedded set of 'critical points', its foreshocks and any subsequent shocks for which it may be a foreshock.

Precise determination of universal finite volume observables in the Gross-Neveu model

Energy Technology Data Exchange (ETDEWEB)

Korzec, T.

2007-01-26

The Gross-Neveu model is a quantum field theory in two space time dimensions that shares many features with quantum chromo dynamics. In this thesis the continuum model and its discretized versions are reviewed and a finite volume renormalization scheme is introduced and tested. Calculations in the limit of infinitely many fermion flavors as well as perturbative computations are carried out. In extensive Monte-Carlo simulations of the one flavor and the four flavor lattice models with Wilson fermions a set of universal finite volume observables is calculated to a high precision. In the one flavor model which is equivalent to the massless Thirring model the continuum extrapolated Monte-Carlo results are confronted with an exact solution of the model. (orig.)

Precise determination of universal finite volume observables in the Gross-Neveu model

International Nuclear Information System (INIS)

Korzec, T.

2007-01-01

The Gross-Neveu model is a quantum field theory in two space time dimensions that shares many features with quantum chromo dynamics. In this thesis the continuum model and its discretized versions are reviewed and a finite volume renormalization scheme is introduced and tested. Calculations in the limit of infinitely many fermion flavors as well as perturbative computations are carried out. In extensive Monte-Carlo simulations of the one flavor and the four flavor lattice models with Wilson fermions a set of universal finite volume observables is calculated to a high precision. In the one flavor model which is equivalent to the massless Thirring model the continuum extrapolated Monte-Carlo results are confronted with an exact solution of the model. (orig.)

A simple perturbative renormalization scheme for supersymmetric gauge theories

International Nuclear Information System (INIS)

Foda, O.E.

1983-01-01

We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of [(p+q)/δ] - delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, #betta# is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously. (orig.)

Poissonian renormalizations, exponentials, and power laws

Science.gov (United States)

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Zero-temperature renormalization method for quantum systems. I. Ising model in a transverse field in one dimension

International Nuclear Information System (INIS)

Jullien, R.; Pfeuty, P.; Fields, J.N.; Doniach, S.

1978-01-01

A zero-temperature real-space renormalization-group method is presented and applied to the quantum Ising model with a transverse field in one dimension. The transition between the low-field and high-field regimes is studied. Magnetization components, spin correlation functions, and critical exponents are derived and checked against the exact results. It is shown that increasing the size of the blocks in the iterative procedure yields more accurate results, especially for the critical ''magnetic'' exponents near the transition

Renormalization group improved Yennie-Frautschi-Suura theory for Z0 physics

International Nuclear Information System (INIS)

Ward, B.F.L.

1987-06-01

Described is a recently developed renormalization group improved version of the program of Yennie, Frautschi and Suura for the exponentiation of infrared divergences in Abelian gauge theories. Particular attention is paid to the relevance of this renormalization group improved exponentiation to Z 0 physics at the SLC and LEP

Renormalization constants for 2-twist operators in twisted mass QCD

International Nuclear Information System (INIS)

Alexandrou, C.; Constantinou, M.; Panagopoulos, H.; Stylianou, F.; Korzec, T.

2011-01-01

Perturbative and nonperturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the nonperturbative evaluation of the one-derivative twist-2 vector and axial-vector operators. Nonperturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing a corresponding to β=3.9, 4.05, 4.20. Subtraction of O(a 2 ) terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to O(a 2 ). The renormalization conditions are defined in the RI ' -MOM scheme, for both perturbative and nonperturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS at 2 GeV using 3-loop perturbative results for the conversion factors.

A shape dynamical approach to holographic renormalization

Energy Technology Data Exchange (ETDEWEB)

Gomes, Henrique [University of California at Davis, Davis, CA (United States); Gryb, Sean [Utrecht University, Institute for Theoretical Physics, Utrecht (Netherlands); Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen (Netherlands); Koslowski, Tim [University of New Brunswick, Fredericton, NB (Canada); Mercati, Flavio; Smolin, Lee [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)

2015-01-01

We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities. (orig.)

Renormalization group treatment of nonrenormalizable interactions

International Nuclear Information System (INIS)

Kazakov, D I; Vartanov, G S

2006-01-01

The structure of the UV divergences in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergences (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. An explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the naive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms

Rota-Baxter algebras and the Hopf algebra of renormalization

Energy Technology Data Exchange (ETDEWEB)

Ebrahimi-Fard, K.

2006-06-15

Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

Rota-Baxter algebras and the Hopf algebra of renormalization

International Nuclear Information System (INIS)

Ebrahimi-Fard, K.

2006-06-01

Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

Quantum statistical mechanics of nonrelativistic membranes: crumpling transition at finite temperature

Science.gov (United States)

Borelli, M. E. S.; Kleinert, H.; Schakel, Adriaan M. J.

2000-03-01

The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to stiffen the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.

Products of composite operators in the exact renormalization group formalism

Science.gov (United States)

Pagani, C.; Sonoda, H.

2018-02-01

We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.

Real space renormalization tecniques for disordered systems

International Nuclear Information System (INIS)

Anda, E.V.

1984-01-01

Real space renormalization techniques are applied to study different disordered systems, with an emphasis on the understanding of the electronic properties of amorphous matter, mainly semiconductors. (Authors) [pt

The renormalization group: scale transformations and changes of scheme

International Nuclear Information System (INIS)

Roditi, I.

1983-01-01

Starting from a study of perturbation theory, the renormalization group is expressed, not only for changes of scale but also within the original view of Stueckelberg and Peterman, for changes of renormalization scheme. The consequences that follow from using that group are investigated. Following a more general point of view a method to obtain an improvement of the perturbative results for physical quantities is proposed. The results obtained with this method are compared with those of other existing methods. (L.C.) [pt

Renormalization of an abelian gauge theory in stochastic quantization

International Nuclear Information System (INIS)

Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.

1987-01-01

The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)

Real space renormalization techniques for disordered systems

International Nuclear Information System (INIS)

Anda, E.V.

1985-01-01

Real Space renormalization techniques are applied to study different disordered systems, with an emphasis on the under-standing of the electronic properties of amorphous matter, mainly semiconductors. (author) [pt

Renormalization group and mayer expansions

International Nuclear Information System (INIS)

Mack, G.

1984-01-01

Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U (1) lattice gauge theory by Gopfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear σ-model, and elsewhere

Renormalization group evolution of Dirac neutrino masses

International Nuclear Information System (INIS)

Lindner, Manfred; Ratz, Michael; Schmidt, Michael Andreas

2005-01-01

There are good reasons why neutrinos could be Majorana particles, but there exist also a number of very good reasons why neutrinos could have Dirac masses. The latter option deserves more attention and we derive therefore analytic expressions describing the renormalization group evolution of mixing angles and of the CP phase for Dirac neutrinos. Radiative corrections to leptonic mixings are in this case enhanced compared to the quark mixings because the hierarchy of neutrino masses is milder and because the mixing angles are larger. The renormalization group effects are compared to the precision of current and future neutrino experiments. We find that, in the MSSM framework, radiative corrections of the mixing angles are for large tan β comparable to the precision of future experiments

Renormalization-group flow of the effective action of cosmological large-scale structures

CERN Document Server

Floerchinger, Stefan

2017-01-01

Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically, the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input ...

Mass renormalization in sine-Gordon model

International Nuclear Information System (INIS)

Xu Bowei; Zhang Yumei

1991-09-01

With a general gaussian wave functional, we investigate the mass renormalization in the sine-Gordon model. At the phase transition point, the sine-Gordon system tends to a system of massless free bosons which possesses conformal symmetry. (author). 8 refs, 1 fig

Renormalization of three-quark operators for baryon distribution amplitudes

Energy Technology Data Exchange (ETDEWEB)

Gruber, Michael

2017-07-01

In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI{sup '}/SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.

Renormalization of three-quark operators for baryon distribution amplitudes

International Nuclear Information System (INIS)

Gruber, Michael

2017-01-01

In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI ' /SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.

Renormalization group and Mayer expansions

International Nuclear Information System (INIS)

Mack, G.

1984-02-01

Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U(1) lattice gauge theory by Goepfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear sigma-model, and elsewhere. (orig.)

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

g-Boson renormalization effects in the interacting Boson model for nondegenerate orbits

Science.gov (United States)

Duval, P. D.; Pittel, S.; Barrett, B. R.; Druce, C. H.

1983-09-01

A nonperturbative model-space truncation procedure is utilized to include the effects of a single g boson on the parameters of the neutron-proton Interacting Boson Model in the realistic case of nondegenerate single-particle orbits. Particular emphasis is given to the single-boson energies ɛdϱ (ϱ = v, π), with numerical results presented for the even isotopes of Hg. Only part of the observed renormalization is obtained. Possible sources of further renormalizations to ɛdϱ are discussed. Results are also presented for the renormalizations of the boson quadrupole parameters κ and χϱ.

Tadpole renormalization and relativistic corrections in lattice NRQCD

Science.gov (United States)

Shakespeare, Norman H.; Trottier, Howard D.

1998-08-01

We make a detailed comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. We renormalize improved gauge-field and NRQCD actions using the mean-link u0,L in the Landau gauge, and using the fourth root of the average plaquette u0,P. Simulations are done for the three quarkonium systems cc¯, bc¯, and bb¯. The hyperfine splittings are computed both at leading [O(MQv4)] and at next-to-leading [O(MQv6)] order in the relativistic expansion, where MQ is the renormalized quark mass, and v2 is the mean-squared velocity. Results are obtained at a large number of lattice spacings, in the range of about 0.14-0.38 fm. A number of features emerge, all of which favor tadpole renormalization using u0,L. This includes a much better scaling behavior of the hyperfine splittings in the three quarkonium systems when u0,L is used. We also find that relativistic corrections to the spin splittings are smaller when u0,L is used, particularly for the cc¯ and bc¯ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about 1 in lattice units. Simulations with u0,L also appear to be better behaved in this context: the bare quark masses turn out to be larger when u0,L is used, compared to when u0,P is used on lattices with comparable spacings. These results also demonstrate the need to go beyond tree-level tadpole improvement for precision simulations.

The renormalization group of relativistic quantum field theory as a set of generalized, spontaneously broken, symmetry transformations

International Nuclear Information System (INIS)

Maris, Th.A.J.

1976-01-01

The renormalization group theory has a natural place in a general framework of symmetries in quantum field theories. Seen in this way, a 'renormalization group' is a one-parametric subset of the direct product of dilatation and renormalization groups. This subset of spontaneously broken symmetry transformations connects the inequivalent solutions generated by a parameter-dependent regularization procedure, as occurs in renormalized perturbation theory. By considering the global, rather than the infinitesimal, transformations, an expression for general vertices is directly obtained, which is the formal solution of exact renormalization group equations [pt

Systematic renormalization of the effective theory of Large Scale Structure

International Nuclear Information System (INIS)

Abolhasani, Ali Akbar; Mirbabayi, Mehrdad; Pajer, Enrico

2016-01-01

A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k 2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.

Fine-grained entanglement loss along renormalization-group flows

International Nuclear Information System (INIS)

Latorre, J.I.; Rico, E.; Luetken, C.A.; Vidal, G.

2005-01-01

We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along renormalization group trajectories from the properties of the vacuum only, without need to study the whole Hamiltonian

Renormalization in Large Momentum Effective Theory of Parton Physics.

Science.gov (United States)

Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong

2018-03-16

In the large-momentum effective field theory approach to parton physics, the matrix elements of nonlocal operators of quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated in lattice quantum chromodynamics as a function of hadron momentum. Using the heavy-quark effective theory formalism, we show a multiplicative renormalization of these operators at all orders in perturbation theory, both in dimensional and lattice regularizations. The result provides a theoretical basis for extracting parton properties through properly renormalized observables in Monte Carlo simulations.

Algebraic renormalization perturbative twisted considerations on topological Yang-Mills theory and on N=2 supersymmetric gauge theories

International Nuclear Information System (INIS)

Fucito, F.; Tanzini, A.; Sorella, S.P.

1997-07-01

The aim of these notes is to provide a simple and pedagogical (as much as possible) introduction to what is nowadays commonly called Algebraic Renormalization. As the same itself let it understand, the Algebraic Renormalization gives a systematic set up in order to analyse the quantum extension of a given set of classical symmetries. The framework is purely algebraic, yielding a complete characterization of all possible anomalies and invariant counterterms without making use of any explicit computation of the Feynman diagrams. This goal is achieved by collecting, with the introduction of suitable ghost fields, all the symmetries into a unique operation summarized by a generalized Slavnov-Taylor (or master equation) identity which is the starting point for the quantum analysis. The Slavnov-Taylor identity allows to define a nilpotent operator whose cohomology classes in the space of the integrated local polynomials in the fields and their derivatives with dimensions bounded by power counting give all nontrivial anomalies and counterterms. I other words, the proof of the renormalizability is reduced to the computation of some cohomology classes. (author)

Probing renormalization group flows using entanglement entropy

International Nuclear Information System (INIS)

Liu, Hong; Mezei, Márk

2014-01-01

In this paper we continue the study of renormalized entanglement entropy introduced in http://dx.doi.org/10.1007/JHEP04(2013)162. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen

Renormalization group flow of the Higgs potential.

Science.gov (United States)

Gies, Holger; Sondenheimer, René

2018-03-06

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).

Temperature dependent quasiparticle renormalization in nickel metal

Energy Technology Data Exchange (ETDEWEB)

Ovsyannikov, Ruslan; Sanchez-Barriga, Jaime; Fink, Joerg; Duerr, Hermann A. [Helmholtz Zentrum Berlin (Germany). BESSY II

2009-07-01

One of the fundamental consequences of electron correlation effects is that the bare particles in solids become 'dressed', i.e. they acquire an increased effective mass and a lifetime. We studied the spin dependent quasiparticle band structure of Ni(111) with high resolution angle resolved photoemission spectroscopy. At low temperatures (50 K) a renormalization of quasiparticle energy and lifetime indicative of electron-phonon coupling is observed in agreement with literature. With increasing temperature we observe a decreasing quasiparticle lifetime at the Fermi level for all probed minority spin bands as expected from electron phonon coupling. Surprisingly the majority spin states behave differently. We actually observe a slightly increased lifetime at room temperature. The corresponding increase in Fermi velocity points to a temperature dependent reduction of the majority spin quasiparticle renormalization.

Two-loop renormalization of quantum gravity simplified

Science.gov (United States)

Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex

2017-02-01

The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

Covariant Derivatives and the Renormalization Group Equation

Science.gov (United States)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

Renormalization group in quantum mechanics

International Nuclear Information System (INIS)

Polony, J.

1996-01-01

The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright copyright 1996 Academic Press, Inc

Renormalized powers of quantum white noise

International Nuclear Information System (INIS)

Accardi, L.; Boukas, A.

2009-01-01

Giving meaning to the powers of the creation and annihilation densities (quantum white noise) is an old and important problem in quantum field theory. In this paper we present an account of some new ideas that have recently emerged in the attempt to solve this problem. We emphasize the connection between the Lie algebra of the renormalized higher powers of quantum white noise (RHPWN), which can be interpreted as a suitably deformed (due to renormalization) current algebra over the 1-mode full oscillator algebra, and the current algebra over the centerless Virasoro (or Witt)-Zamolodchikov-ω ∞ Lie algebras of conformal field theory. Through a suitable definition of the action on the vacuum vector we describe how to obtain a Fock representation of all these algebras. We prove that the restriction of the vacuum to the abelian subalgebra generated by the field operators gives an infinitely divisible process whose marginal distribution is the beta (or continuous binomial). (authors)

Infinities in Quantum Field Theory and in Classical Computing: Renormalization Program

Science.gov (United States)

Manin, Yuri I.

Introduction. The main observable quantities in Quantum Field Theory, correlation functions, are expressed by the celebrated Feynman path integrals. A mathematical definition of them involving a measure and actual integration is still lacking. Instead, it is replaced by a series of ad hoc but highly efficient and suggestive heuristic formulas such as perturbation formalism. The latter interprets such an integral as a formal series of finite-dimensional but divergent integrals, indexed by Feynman graphs, the list of which is determined by the Lagrangian of the theory. Renormalization is a prescription that allows one to systematically "subtract infinities" from these divergent terms producing an asymptotic series for quantum correlation functions. On the other hand, graphs treated as "flowcharts", also form a combinatorial skeleton of the abstract computation theory. Partial recursive functions that according to Church's thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops. In this paper I argue that such infinities can be addressed in the same way as Feynman divergences. More details can be found in [9,10].

Can renormalization group flow end in a Big Mess?

International Nuclear Information System (INIS)

Morozov, Alexei; Niemi, Antti J.

2003-01-01

The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point is reminiscent of self-similarity in autonomous flows towards attractors. Motivated by such analogies we propose that besides isolated fixed points, the couplings in a renormalizable field theory may also flow towards more general, even fractal attractors. This could lead to Big Mess scenarios in applications to multiphase systems, from spin-glasses and neural networks to fundamental string (M?) theory. We consider various general aspects of such chaotic flows. We argue that they pose no obvious contradictions with the known properties of effective actions, the existence of dissipative Lyapunov functions, and even the strong version of the c-theorem. We also explain the difficulties encountered when constructing effective actions with chaotic renormalization group flows and observe that they have many common virtues with realistic field theory effective actions. We conclude that if chaotic renormalization group flows are to be excluded, conceptually novel no-go theorems must be developed

Renormalization of Magnetic Excitations in Praseodymium

DEFF Research Database (Denmark)

Lindgård, Per-Anker

1975-01-01

The magnetic exciton renormalization and soft-mode behaviour as the temperature approaches zero of the singlet-doublet magnet (dhcp)pr are accounted for by a selfconsistent rpa theory with no adjustable parameters. The crystal-field splitting between the ground state and the doublet is d=3.74 mev...

The large-Nc renormalization group

International Nuclear Information System (INIS)

Dorey, N.

1995-01-01

In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N c , limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N c , selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N c . We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius Λ -1 (Λ being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r ≤ Λ -1 . The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-Δ hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N c , renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as Λ → ∞

Strong-Weak CP Hierarchy from Non-Renormalization Theorems

Energy Technology Data Exchange (ETDEWEB)

Hiller, Gudrun

2002-01-28

We point out that the hierarchy between the measured values of the CKM phase and the strong CP phase has a natural origin in supersymmetry with spontaneous CP violation and low energy supersymmetry breaking. The underlying reason is simple and elegant: in supersymmetry the strong CP phase is protected by an exact non-renormalization theorem while the CKM phase is not. We present explicit examples of models which exploit this fact and discuss corrections to the non-renormalization theorem in the presence of supersymmetry breaking. This framework for solving the strong CP problem has generic predictions for the superpartner spectrum, for CP and flavor violation, and predicts a preferred range of values for electric dipole moments.

Renormalization-group study of the four-body problem

International Nuclear Information System (INIS)

Schmidt, Richard; Moroz, Sergej

2010-01-01

We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.

Running with rugby balls: bulk renormalization of codimension-2 branes

Science.gov (United States)

Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.

2013-01-01

We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

Nuclear matter kinetic coefficients and damping of finite nuclear collective modes

International Nuclear Information System (INIS)

Toledo Piza, A.F.R. de.

1986-06-01

By carrying the general description of one-body observables beyond the mean-field approximation, those correlation terms responsible for Kinetic phenomena and those involved in the renormalization of the G-matrix mean-field in finite nuclei are identified. A Kinetic equation for the one-body density is obtained. Estimates for transport coefficients and for the damping of zero sound are obtained which point to the inadequacy of hydrodynamical descriptions of collective nuclear modes and indicate that collisional damping in large nuclei may account for one or a few tenths of the observed widths. (S.D.) [pt

Structural impact on the eigenenergy renormalization for carbon and silicon allotropes and boron nitride polymorphs

Science.gov (United States)

Tutchton, Roxanne; Marchbanks, Christopher; Wu, Zhigang

2018-05-01

The phonon-induced renormalization of electronic band structures is investigated through first-principles calculations based on the density functional perturbation theory for nine materials with various crystal symmetries. Our results demonstrate that the magnitude of the zero-point renormalization (ZPR) of the electronic band structure is dependent on both crystal structure and material composition. We have performed analysis of the electron-phonon-coupling-induced renormalization for two silicon (Si) allotropes, three carbon (C) allotropes, and four boron nitride (BN) polymorphs. Phonon dispersions of each material were computed, and our analysis indicates that materials with optical phonons at higher maximum frequencies, such as graphite and hexagonal BN, have larger absolute ZPRs, with the exception of graphene, which has a considerably smaller ZPR despite having phonon frequencies in the same range as graphite. Depending on the structure and material, renormalizations can be comparable to the GW many-body corrections to Kohn-Sham eigenenergies and, thus, need to be considered in electronic structure calculations. The temperature dependence of the renormalizations is also considered, and in all materials, the eigenenergy renormalization at the band gap and around the Fermi level increases with increasing temperature.

Renormalization and Interaction in Quantum Field Theory

International Nuclear Information System (INIS)

RATSIMBARISON, H.M.

2008-01-01

This thesis works on renormalization in quantum field theory (QFT), in order to show the relevance of some mathematical structures as C*-algebraic and probabilistic structures. Our work begins with a study of the path integral formalism and the Kreimer-Connes approach in perturbative renormalization, which allows to situate the statistical nature of QFT and to appreciate the ultra-violet divergence problem of its partition function. This study is followed by an emphasis of the presence of convolution products in non perturbative renormalisation, through the construction of the Wilson effective action and the Legendre effective action. Thanks to these constructions and the definition of effective theories according J. Polchinski, the non perturbative renormalization shows in particular the general approach of regularization procedure. We begin the following chapter with a C*-algebraic approach of the scale dependence of physical theories by showing the existence of a hierarchy of commutative spaces of states and its compatibility with the fiber bundle formulation of classical field theory. Our Hierarchy also allows us to modelize the notion of states and particles. Finally, we develop a probabilistic construction of interacting theories starting from simple model, a Bernoulli random processes. We end with some arguments on the applicability of our construction -such as the independence between the free and interacting terms and the possibility to introduce a symmetry group wich will select the type of interactions in quantum field theory. [fr

Renormalized G-convolution of n-point functions in quantum field theory. I. The Euclidean case

International Nuclear Information System (INIS)

Bros, Jacques; Manolessou-Grammaticou, Marietta.

1977-01-01

The notion of Feynman amplitude associated with a graph G in perturbative quantum field theory admits a generalized version in which each vertex v of G is associated with a general (non-perturbative) nsub(v)-point function Hsup(nsub(v)), nsub(v) denoting the number of lines which are incident to v in G. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle's G-convolution procedure. The authors propose a generalization of G-convolution which includes the case when the functions Hsup(nsub(v)) are not integrable at infinity but belong to a suitable class of slowly increasing functions. A finite part of the G-convolution integral is then defined through an algorithm which closely follows Zimmermann's renormalization scheme. The case of Euclidean four-momentum configurations is only treated

QCD: Renormalization for the practitioner

International Nuclear Information System (INIS)

Pascual, P.; Tarrach, R.

1984-01-01

These notes correspond to a GIFT (Grupo Interuniversitario de Fisica Teorica) course which was given by us in autumn 1983 at the University of Barcelona. Their main subject is renormalization in perturbative QCD and only the last chapter goes beyond perturbation theory. They are essentially self contained and their aim is to teach the student the techniques of perturbative QCD and the QCD sum rules. (orig./HSI)

Probabilistic finite elements

Science.gov (United States)

Belytschko, Ted; Wing, Kam Liu

1987-01-01

In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.

A renormalization group invariant line and an infrared attractive top-Higgs mass relation

International Nuclear Information System (INIS)

Schrempp, B.; Schrempp, F.

1992-10-01

The renormalization group equations (RGE's) of the Standard Model at one loop in terms of the gauge couplings g 1,2,3, the top Yukawa coupling g t and the scalar self coupling λ are reexamined. For g 1,2 = 0, the general solution of the RGE's is obtained analytically in terms of an interesting special solution for the ratio λ/g 2 t as function of the ratio g 2 t /g 2 3 which i) represents an RG invariant line which is strongly infrared attractive ii) interpolates all known quasi-fixed points and iii) is finite for large g 2 t /g 2 3 (ultraviolet limit). All essential features survive for g 1,2 ≠ 0. The invariant line translates into an infrared attractive top-Higgs mass relation, which e.g. associates to the top masses m t = 130/145/200 GeV the Higgs masses m H ≅ 68-90/103-115/207 GeV, respectively. (orig.)

New renormalization group approach to multiscale problems

Energy Technology Data Exchange (ETDEWEB)

Einhorn, M B; Jones, D R.T.

1984-02-27

A new renormalization group is presented which exploits invariance with respect to more than one scale. The method is illustrated by a simple model, and future applications to fields such as critical phenomena and supersymmetry are speculated upon.

Renormalization Group Invariance of the Pole Mass in the Multi-Higgs System

Science.gov (United States)

Kim, Chungku

2018-06-01

We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of gauge fixing conditions. The pole mass, when expressed in terms of the Lagrangian parameters, turns out to be invariant under the renormalization group with the beta and gamma functions of the symmetric phase.

Reduction of Couplings: Applications in Finite Theories and the MSSM

CERN Document Server

Mondragón, Myriam; Tracas, Nick; Zoupanos, George

2017-01-01

The method of reduction of couplings is applied to a Finite Unified Theory and in the MSSM.We search for renormalization group invariant relations among couplings of a renormalizable theory which holds to all orders in perturbation theory. The method leads to relations, at the unification scale, between gauge and Yukawa couplings (in the dimensionless sectors of the theory) and relations among the couplings of the trilinear terms and the Yukawa couplings, as well as a sum rule among the scalar masses and the gaugino mass (in the soft breaking sector). In the Finite Unified Theory model we predict, with remarkable agreement with the experiment, the masses of the top and bottom quarks while our predictions for the light Higgs mass and the rest supersymmetric spectrum masses are in comfortable agreement with the LHC bounds on Higgs and supersymmetric particles. In the case of the reduced MSSM the predictions are less successful but recent improvements in the code used to calculate the Higgs masses give promises ...

Renormalization group and the superconducting susceptibility of a Fermi liquid

International Nuclear Information System (INIS)

Parameswaran, S. A.; Sondhi, S. L.; Shankar, R.

2010-01-01

A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.

Re-Normalization Method of Doppler Lidar Signal for Error Reduction

Energy Technology Data Exchange (ETDEWEB)

Park, Nakgyu; Baik, Sunghoon; Park, Seungkyu; Kim, Donglyul [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Kim, Dukhyeon [Hanbat National Univ., Daejeon (Korea, Republic of)

2014-05-15

In this paper, we presented a re-normalization method for the fluctuations of Doppler signals from the various noises mainly due to the frequency locking error for a Doppler lidar system. For the Doppler lidar system, we used an injection-seeded pulsed Nd:YAG laser as the transmitter and an iodine filter as the Doppler frequency discriminator. For the Doppler frequency shift measurement, the transmission ratio using the injection-seeded laser is locked to stabilize the frequency. If the frequency locking system is not perfect, the Doppler signal has some error due to the frequency locking error. The re-normalization process of the Doppler signals was performed to reduce this error using an additional laser beam to an Iodine cell. We confirmed that the renormalized Doppler signal shows the stable experimental data much more than that of the averaged Doppler signal using our calibration method, the reduced standard deviation was 4.838 Χ 10{sup -3}.

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

Quark-mixing renormalization effects on the W-boson partial decay widths

International Nuclear Information System (INIS)

Almasy, A.A.; Kniehl, B.A.; Sirlin, A.

2008-10-01

We briefly review existing proposals for the renormalization of the Cabibbo- Kobayashi-Maskawa matrix and study their numerical effects on the W-boson partial decay widths. The differences between the decay widths predicted by the various renormalization schemes are generally negligible, while their deviations from the MS results are very small, except for W + → u anti b and W + →c anti b, where they reach approximately 4%. (orig.)

All-order renormalization of propagator matrix for Majorana fermions with inter-generation mixing

International Nuclear Information System (INIS)

Kniehl, Bernd A.

2014-04-01

We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. We present closed analytic expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions, as well as their expansions through two loops. In the case of stable Majorana fermions, the well-known one-loop results are recovered.

Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing

Science.gov (United States)

Baumgarten, Lorenz; Kierfeld, Jan

2018-05-01

We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017), 10.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy

Functional renormalization group study of fluctuation effects in fermionic superfluids

Energy Technology Data Exchange (ETDEWEB)

Eberlein, Andreas

2013-03-22

This thesis is concerned with ground state properties of two-dimensional fermionic superfluids. In such systems, fluctuation effects are particularly strong and lead for example to a renormalization of the order parameter and to infrared singularities. In the first part of this thesis, the fermionic two-particle vertex is analysed and the fermionic renormalization group is used to derive flow equations for a decomposition of the vertex in charge, magnetic and pairing channels. In the second part, the channel-decomposition scheme is applied to various model systems. In the superfluid state, the fermionic two-particle vertex develops rich and singular dependences on momentum and frequency. After simplifying its structure by exploiting symmetries, a parametrization of the vertex in terms of boson-exchange interactions in the particle-hole and particle-particle channels is formulated, which provides an efficient description of the singular momentum and frequency dependences. Based on this decomposition of the vertex, flow equations for the effective interactions are derived on one- and two-loop level, extending existing channel-decomposition schemes to (i) the description of symmetry breaking in the Cooper channel and (ii) the inclusion of those two-loop renormalization contributions to the vertex that are neglected in the Katanin scheme. In the second part, the superfluid ground state of various model systems is studied using the channel-decomposition scheme for the vertex and the flow equations. A reduced model with interactions in the pairing and forward scattering channels is solved exactly, yielding insights into the singularity structure of the vertex. For the attractive Hubbard model at weak coupling, the momentum and frequency dependence of the two-particle vertex and the frequency dependence of the self-energy are determined on one- and two-loop level. Results for the suppression of the superfluid gap by fluctuations are in good agreement with the literature

PyR@TE. Renormalization group equations for general gauge theories

Science.gov (United States)

Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

2014-03-01

Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer

On the renormalization of operator products: the scalar gluonic case

International Nuclear Information System (INIS)

Zoller, Max F.

2016-01-01

In this paper we study the renormalization of the product of two operators O 1 =−(1/4)G μν G μν in QCD. An insertion of two such operators O 1 (x)O 1 (0) into a Greens function produces divergent contact terms for x→0. In the course of the computation of the operator product expansion (OPE) of the correlator of two such operators i∫ d 4 x e iqx T{ O 1 (x)O 1 (0)} to three-loop order http://dx.doi.org/10.1007/JHEP12(2012)119; http://dx.doi.org/10.1007/JHEP10(2014)169 we discovered that divergent contact terms remain not only in the leading Wilson coefficient C 0 , which is just the VEV of the correlator, but also in the Wilson coefficient C 1 in front of O 1 . As this correlator plays an important role for example in QCD sum rules a full understanding of its renormalization is desireable. This work explains how the divergences encountered in higher orders of an OPE of this correlator should be absorbed in counterterms and derives an additive renormalization constant for C 1 from first principles and to all orders in perturnbation theory. The method to derive the renormalization of this operator product is an extension of the ideas of V. Spiridonov, Anomalous dimension of g μν 2 and β-function, Preprint IYAI-P-0378 (1984). and can be generalized to other cases.

RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

International Nuclear Information System (INIS)

Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.

2010-01-01

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

Renormalization group fixed points of foliated gravity-matter systems

Energy Technology Data Exchange (ETDEWEB)

Biemans, Jorn [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Platania, Alessia [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Department of Physics and Astronomy, University of Catania,Via S. Sofia 63, 95123 Catania (Italy); INFN, Catania section,Via S. Sofia 64, 95123, Catania (Italy); INAF, Catania Astrophysical Observatory,Via S. Sofia 78, 95123, Catania (Italy); Saueressig, Frank [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands)

2017-05-17

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) “time”-direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton’s constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d{sub g}, d{sub λ}. We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

Science.gov (United States)

Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

2016-07-01

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

Renormalization-group decimation technique for spectra, wave-functions and density of states

International Nuclear Information System (INIS)

Wiecko, C.; Roman, E.

1983-09-01

The Renormalization Group decimation technique is very useful for problems described by 1-d nearest neighbour tight-binding model with or without translational invariance. We show how spectra, wave-functions and density of states can be calculated with little numerical work from the renormalized coefficients upon iteration. The results of this new procedure are verified using the model of Soukoulis and Economou. (author)

Renormalization Group scale-setting in astrophysical systems

Science.gov (United States)

Domazet, Silvije; Štefančić, Hrvoje

2011-09-01

A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

Renormalization Group scale-setting in astrophysical systems

International Nuclear Information System (INIS)

Domazet, Silvije; Stefancic, Hrvoje

2011-01-01

A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

Perturbative renormalization of composite operators via flow equations. Pt. 1

Energy Technology Data Exchange (ETDEWEB)

Keller, G. (Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany). Werner-Heisenberg-Inst. fuer Physik); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)

1992-09-01

We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive {Phi}{sub 4}{sup 4} theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.).

Perturbative renormalization of composite operators via flow equations. Pt. 1

International Nuclear Information System (INIS)

Keller, G.; Kopper, C.

1992-01-01

We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive Φ 4 4 theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.)

Justification of the zeta-function renormalization in rigid string model

International Nuclear Information System (INIS)

Nesterenko, V.V.; Pirozhenko, I.G.

1997-01-01

A consistent procedure for regularization of divergences and for the subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov-Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein-Hurwitz zeta-functions is given. A spectral representation for the renormalized string energy at zero temperature is derived, which enables one to find the Casimir energy in this string model at nonzero temperature very easy

Vacuum polarization and renormalized charge in ν-dimensions

International Nuclear Information System (INIS)

Marinho Junior, R.M.; Lucinda, J.

1984-01-01

The expression for the vacuum polarization is obtained for any momentum transfer in ν dimensions. Using the Wilson loop for QED, the renormalized electric charge in ν dimensions is calculated. (Author) [pt

Renormalization Group Functional Equations

CERN Document Server

Curtright, Thomas L

2011-01-01

Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.

Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

Energy Technology Data Exchange (ETDEWEB)

Green, Jeremy; Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2017-07-15

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

International Nuclear Information System (INIS)

Green, Jeremy; Jansen, Karl; Steffens, Fernanda

2017-07-01

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Functional-derivative study of the Hubbard model. III. Fully renormalized Green's function

International Nuclear Information System (INIS)

Arai, T.; Cohen, M.H.

1980-01-01

The functional-derivative method of calculating the Green's function developed earlier for the Hubbard model is generalized and used to obtain a fully renormalized solution. Higher-order functional derivatives operating on the basic Green's functions, G and GAMMA, are all evaluated explicitly, thus making the solution applicable to the narrow-band region as well as the wide-band region. Correction terms Phi generated from functional derivatives of equal-time Green's functions of the type delta/sup n/ /deltaepsilon/sup n/, etc., with n > or = 2. It is found that the Phi's are, in fact, renormalization factors involved in the self-energy Σ and that the structure of the Phi's resembles that of Σ and contains the same renormalization factors Phi. The renormalization factors Phi are shown to satisfy a set of equations and can be evaluated self-consistently. In the presence of the Phi's, all difficulties found in the previous results (papers I and II) are removed, and the energy spectrum ω can now be evaluated for all occupations n. The Schwinger relation is the only basic relation used in generating this fully self-consistent Green's function, and the Baym-Kadanoff continuity condition is automatically satisfied

Generalized Callan-Symanzik equations and the Renormalization Group

International Nuclear Information System (INIS)

MacDowell, S.W.

1975-01-01

A set of generalized Callan-Symanzik equations derived by Symanzik, relating Green's functions with arbitrary number of mass insertions, is shown be equivalent to the new Renormalization Group equation proposed by S. Weinberg

Exact renormalization group as a scheme for calculations

International Nuclear Information System (INIS)

Mack, G.

1985-10-01

In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)

Renormalization group and critical phenomena

International Nuclear Information System (INIS)

Ji Qing

2004-01-01

The basic clue and the main steps of renormalization group method used for the description of critical phenomena is introduced. It is pointed out that this method really reflects the most important physical features of critical phenomena, i.e. self-similarity, and set up a practical solving method from it. This way of setting up a theory according to the features of the physical system is really a good lesson for today's physicists. (author)

Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears

Science.gov (United States)

Panagopoulos, Haralambos; Spanoudes, Gregoris

2018-03-01

In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet (Σfψ¯fΓψf', f : flavor index) and nonsinglet (ψ¯f1Γψf2,f1 ≠ f2) bilinear quark operators (where Γ = 𝟙, γ5, γ µ, γ5 γ µ, γ5 σµv on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, using Symanzik improved gluons and staggered fermions with twice stout-smeared links. The stout smearing procedure is also applied to the definition of bilinear operators. A significant part of this work is the development of a method for treating some new peculiar divergent integrals stemming from the staggered formalism. Our results can be combined with precise simulation results for the renormalization factors of the nonsinglet operators, in order to obtain an estimate of the renormalization factors for the singlet operators. The results have been published in Physical Review D [1].

Effect of dislocation pile-up on size-dependent yield strength in finite single-crystal micro-samples

Energy Technology Data Exchange (ETDEWEB)

Pan, Bo; Shibutani, Yoji, E-mail: sibutani@mech.eng.osaka-u.ac.jp [Department of Mechanical Engineering, Osaka University, Suita 565-0871 (Japan); Zhang, Xu [State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi' an Jiaotong University, Xi' an 710049 (China); School of Mechanics and Engineering Science, Zhengzhou University, Zhengzhou 450001 (China); Shang, Fulin [State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi' an Jiaotong University, Xi' an 710049 (China)

2015-07-07

Recent research has explained that the steeply increasing yield strength in metals depends on decreasing sample size. In this work, we derive a statistical physical model of the yield strength of finite single-crystal micro-pillars that depends on single-ended dislocation pile-up inside the micro-pillars. We show that this size effect can be explained almost completely by considering the stochastic lengths of the dislocation source and the dislocation pile-up length in the single-crystal micro-pillars. The Hall–Petch-type relation holds even in a microscale single-crystal, which is characterized by its dislocation source lengths. Our quantitative conclusions suggest that the number of dislocation sources and pile-ups are significant factors for the size effect. They also indicate that starvation of dislocation sources is another reason for the size effect. Moreover, we investigated the explicit relationship between the stacking fault energy and the dislocation “pile-up” effect inside the sample: materials with low stacking fault energy exhibit an obvious dislocation pile-up effect. Our proposed physical model predicts a sample strength that agrees well with experimental data, and our model can give a more precise prediction than the current single arm source model, especially for materials with low stacking fault energy.

Finite-amplitude, pulsed, ultrasonic beams

Science.gov (United States)

Coulouvrat, François; Frøysa, Kjell-Eivind

An analytical, approximate solution of the inviscid KZK equation for a nonlinear pulsed sound beam radiated by an acoustic source with a Gaussian velocity distribution, is obtained by means of the renormalization method. This method involves two steps. First, the transient, weakly nonlinear field is computed. However, because of cumulative nonlinear effects, that expansion is non-uniform and breaks down at some distance away from the source. So, in order to extend its validity, it is re-written in a new frame of co-ordinates, better suited to following the nonlinear distorsion of the wave profile. Basically, the nonlinear coordinate transform introduces additional terms in the expansion, which are chosen so as to counterbalance the non-uniform ones. Special care is devoted to the treatment of shock waves. Finally, comparisons with the results of a finite-difference scheme turn out favorable, and show the efficiency of the method for a rather large range of parameters.

A non-renormalization theorem for conformal anomalies

International Nuclear Information System (INIS)

Petkou, Anastasios; Skenderis, Kostas

1999-01-01

We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields

Functional renormalization group approach to the two dimensional Bose gas

Energy Technology Data Exchange (ETDEWEB)

Sinner, A; Kopietz, P [Institut fuer Theoretische Physik, Universitaet Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt (Germany); Hasselmann, N [International Center for Condensed Matter Physics, Universidade de BrasIlia, Caixa Postal 04667, 70910-900 BrasIlia, DF (Brazil)], E-mail: hasselma@itp.uni-frankfurt.de, E-mail: sinner@itp.uni-frankfurt.de

2009-02-01

We investigate the small frequency and momentum structure of the weakly interacting Bose gas in two dimensions using a functional renormalization group approach. The flow equations are derived within a derivative approximation of the effective action up to second order in spatial and temporal variables and investigated numerically. The truncation we employ is based on the perturbative structure of the theory and is well described as a renormalization group enhanced perturbation theory. It allows to calculate corrections to the Bogoliubov spectrum and to investigate the damping of quasiparticles. Our approach allows to circumvent the divergences which plague the usual perturbative approach.

Closed-form irreducible differential formulations of the Wilson renormalization group

International Nuclear Information System (INIS)

Vvedensky, D.D.; Chang, T.S.; Nicoll, J.F.

1983-01-01

We present a detailed derivation of the one-particle--irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order epsilon 2 the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and eta to order epsilon 2 by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator

Renormalization of non-abelian gauge theories in curved space-time

International Nuclear Information System (INIS)

Freeman, M.D.

1984-01-01

We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe

Renormalization group approach to a p-wave superconducting model

International Nuclear Information System (INIS)

Continentino, Mucio A.; Deus, Fernanda; Caldas, Heron

2014-01-01

We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.

Extending the range of real time density matrix renormalization group simulations

Science.gov (United States)

Kennes, D. M.; Karrasch, C.

2016-03-01

We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ 〉 and operators A in the evaluation of 〈A〉ψ(t) = 〈 ψ | A(t) | ψ 〉 . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics 〈A〉ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.

A rigorous treatment of the lattice renormalization problem of f$_{B}$

CERN Document Server

Boucaud, P; Micheli, J; Pène, O; Rossi, G C; Boucaud, Ph.

1993-01-01

The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $\\alpha_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ t...

Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions

DEFF Research Database (Denmark)

Altenkamp, Lukas; Dittmaier, Stefan; Rzehak, Heidi

2017-01-01

We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization conditions as far as possible and on M S ¯ prescriptions for th...

Nucleation of the lamellar phase from the disordered phase of the renormalized Landau-Brazovskii model

Science.gov (United States)

Carilli, Michael F.; Delaney, Kris T.; Fredrickson, Glenn H.

2018-02-01

Using the zero-temperature string method, we investigate nucleation of a stable lamellar phase from a metastable disordered phase of the renormalized Landau-Brazovskii model at parameters explicitly connected to those of an experimentally accessible diblock copolymer melt. We find anisotropic critical nuclei in qualitative agreement with previous experimental and analytic predictions; we also find good quantitative agreement with the predictions of a single-mode analysis. We conduct a thorough search for critical nuclei containing various predicted and experimentally observed defect structures. The predictions of the renormalized model are assessed by simulating the bare Landau-Brazovskii model with fluctuations. We find that the renormalized model makes reasonable predictions for several important quantities, including the order-disorder transition (ODT). However, the critical nucleus size depends sharply on proximity to the ODT, so even small errors in the ODT predicted by the renormalized model lead to large errors in the predicted critical nucleus size. We conclude that the renormalized model is a poor tool to study nucleation in the fluctuating Landau-Brazovskii model, and recommend that future studies work with the fluctuating bare model directly, using well-chosen collective variables to investigate kinetic pathways in the disorder → lamellar transition.

Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED

International Nuclear Information System (INIS)

Goeckeler, M.; Horsley, R.; Rakow, P.; Schierholz, G.; Sommer, R.

1992-01-01

We investigate the ultra-violet behavior of non-compact lattice QED with light staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second-order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik β-function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. We evaluate the maximum value of the cut-off as a function of the renormalized charge. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action with mean-field critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is non-interacting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for samll renormalized charges. (orig.)

Perturbative renormalization of QED via flow equations

International Nuclear Information System (INIS)

Keller, G.; Kopper, C.

1991-01-01

We prove the perturbative renormalizability of euclidean QED 4 with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.)

A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

OpenAIRE

SASAKURA, NAOKI

2010-01-01

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

Neutral currents and electromagnetic renormalization of the vector part of neutrino weak interaction

International Nuclear Information System (INIS)

Folomeshkin, V.N.

1976-01-01

The nature and properties of neutral currents in neutrino processes at high energies are theoretically investigated. Electronagmetic renormalization of diagonal ((νsub(e)e(νsub(e)e) and (νsub(μ)μ)(νsub(μ)μ)) and nondiagonal ((νsub(e)μ)(νsub(e)μ)) interactions is discussed in terms of the universal fourfermion interaction model. It is shown that electromagnetic renormalization of neutrino vector interaction caused an effective appearance of vector neutral currents with photon isotopic structure. The value for the interaction constant is unambigously defined by the ratio of the total cross-section for electron-positron annihilation into muonic pairs. Interaction (renormalization) constants for neutral currents are pointed out to be always smaller than interaction constants for charge currents

Generalized Hubbard Hamiltonian: renormalization group approach

International Nuclear Information System (INIS)

Cannas, S.A.; Tamarit, F.A.; Tsallis, C.

1991-01-01

We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs

E-cigarette marketing and older smokers: road to renormalization.

Science.gov (United States)

Cataldo, Janine K; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

2015-05-01

To describe older smokers' perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking.

Perturbative renormalization of QED via flow equations

Energy Technology Data Exchange (ETDEWEB)

Keller, G. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany)); Kopper, C. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany) Inst. fuer Theoretische Physik, Univ. Goettingen (Germany))

1991-12-19

We prove the perturbative renormalizability of euclidean QED{sub 4} with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.).

Renormalization (and power counting) of effective field theories for the nuclear force

International Nuclear Information System (INIS)

Timoteo, Varese S.; Szpigel, Sergio; Duraes, Francisco O.

2011-01-01

The most common scheme used to regularize the Lippman-Schwinger (LS) equation is to introduce a sharp or smooth regularizing function that suppresses the contributions from the potential matrix elements for momenta larger than a given cutoff scale, which separates high-energy/short-distance scales and low-energy/long-distance scales, thus eliminating the ultraviolet divergences in the momentum integrals. Then, one needs determine the strengths of the contact interactions, the so called low-energy constants (LEC), by fitting a set of low-energy scattering data. Once the LECs are fixed for a given cutoff, the LS equation can be solved to evaluate other observables. Such a procedure, motivated by Wilsons renormalization group, relies on the fundamental premise of EFT that physics at low-energy/long-distance scales is insensitive with respect to the details of the dynamics at high-energy/short-distance scales, i.e. the relevant high-energy/short- distance effects for describing the low-energy observables can be captured in the cutoff-dependent LECs. The NN interaction can be considered properly renormalized when the calculated observables are independent of the cutoff scale within the range of validity of the ChEFT or involves a small residual cutoff dependence due to the truncation of the chiral expansion. In the language of Wilsons renormalization group, this means that the LECs must run with the cutoff scale in such a way that the scattering amplitude becomes renormalization group invariant (RGI). Here we consider pionless EFT up to NNLO and chiral EFT up to NNLO and use a subtractive renormalization scheme to describe the NN scattering channels with. We fix the strength of the contact interactions at a reference scale, chosen to be the one the provides the best fit, and then evolve the driving terms with a non-relativistic Callan-Symanzik equation to slide the renormalization scale. By computing phase shift relative differences, we show that the method is RGI. We

Renormalization group treatment for spin waves in the randomly disordered Heisenberg chain

International Nuclear Information System (INIS)

Chaves, C.M.; Koiller, B.

1983-03-01

Local densities of states in the randomly disordered binary quantum Heisenberg chain using a generalization of a recently developed approach based on renormalization group ideas are calculated. It envolves decimating alternate apins along the chain in such a way as to obtain recursion relations to describe the renormalized set of Green's function equations of motion. The densities of states are richly structured, indicating that the method takes into account compositional fluctuations of arbitrary range. (Author) [pt

Renormalization group flows and continual Lie algebras

International Nuclear Information System (INIS)

Bakas, Ioannis

2003-01-01

We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by (d/dt;1), with anti-symmetric Cartan kernel K(t,t') = δ'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N vertical bar N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Baecklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra (d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown. (author)

The density-matrix renormalization group: a short introduction.

Science.gov (United States)

Schollwöck, Ulrich

2011-07-13

The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

One-loop renormalization of Lee-Wick gauge theory

International Nuclear Information System (INIS)

Grinstein, Benjamin; O'Connell, Donal

2008-01-01

We examine the renormalization of Lee-Wick gauge theory to one-loop order. We show that only knowledge of the wave function renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theory than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.

Renormalization and asymptotic freedom in quantum gravity

International Nuclear Information System (INIS)

Tomboulis, E.T.

1984-01-01

The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)

Renormalization in quantum field theory and the Riemann-Hilbert problem. I. Hopf algebra structure of graphs and the main theorem

International Nuclear Information System (INIS)

Connes, A.; Kreimer, D.

2000-01-01

This paper gives a complete selfcontained proof of our result (1999) showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra H which is commutative asan algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra G whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of H. We show then that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop γ(z) element of G, z element of C, where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ + of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. (orig.)

Optimal renormalization scales and commensurate scale relations

International Nuclear Information System (INIS)

Brodsky, S.J.; Lu, H.J.

1996-01-01

Commensurate scale relations relate observables to observables and thus are independent of theoretical conventions, such as the choice of intermediate renormalization scheme. The physical quantities are related at commensurate scales which satisfy a transitivity rule which ensures that predictions are independent of the choice of an intermediate renormalization scheme. QCD can thus be tested in a new and precise way by checking that the observables track both in their relative normalization and in their commensurate scale dependence. For example, the radiative corrections to the Bjorken sum rule at a given momentum transfer Q can be predicted from measurements of the e+e - annihilation cross section at a corresponding commensurate energy scale √s ∝ Q, thus generalizing Crewther's relation to non-conformal QCD. The coefficients that appear in this perturbative expansion take the form of a simple geometric series and thus have no renormalon divergent behavior. The authors also discuss scale-fixed relations between the threshold corrections to the heavy quark production cross section in e+e - annihilation and the heavy quark coupling α V which is measurable in lattice gauge theory

Renormalization analysis of catalytic Wright-Fisher diffusions

Czech Academy of Sciences Publication Activity Database

Swart, Jan M.; Fleischmann, K.

2006-01-01

Roč. 2006, č. 11 (2006), s. 585-654 ISSN 1083-6489 R&D Projects: GA ČR GA201/06/1323 Institutional research plan: CEZ:AV0Z10750506 Keywords : renormalization * catalytic Wright-Fisher diffusion * embedded particle system * extinction * unbounded growth * interacting diffusions * universality Subject RIV: BA - General Mathematics Impact factor: 0.676, year: 2006

Renormalization group approach to causal bulk viscous cosmological models

International Nuclear Information System (INIS)

Belinchon, J A; Harko, T; Mak, M K

2002-01-01

The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, the causal evolution equation of the bulk viscous pressure and the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale-invariant fixed point, thereby obtaining the long-time behaviour of the scale factor

E-cigarette Marketing and Older Smokers: Road to Renormalization

Science.gov (United States)

Cataldo, Janine K.; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

2015-01-01

Objectives To describe older smokers’ perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Methods Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Results Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. Conclusions To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking. PMID:25741681

A key heterogeneous structure of fractal networks based on inverse renormalization scheme

Science.gov (United States)

Bai, Yanan; Huang, Ning; Sun, Lina

2018-06-01

Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.

Renormalization group aspects of 3-dimensional Pure U(1) lattice gauge theory

International Nuclear Information System (INIS)

Gopfert, M.; Mack, G.

1983-01-01

A few surprises in a recent study of the 3-dimensional pure U(1) lattice gauge theory model, from the point of view of the renormalization group theory, are discussed. Since the gauge group U(1) of this model is abelian, the model is subject to KramersWannier duality transformation. One obtains a ferromagnet with a global symmetry group Z. The duality transformation shows that the surface tension alpha of the model equals the strong tension of the U(1) gauge model. A theorem to represent the true asymptotic behaviour of alpha is derived. A second theorem considers the correlation functions. Discrepiancies between the theorems result in a solution that ''is regarded as a catastrophe'' in renormalization group theory. A lesson is drawn: To choose a good block spin in a renormalization group procedure, know what the low lying excitations of the theory are, to avoid integrating some of them by mischief

Finite and Gauge-Yukawa unified theories: Theory and predictions

International Nuclear Information System (INIS)

Kobayashi, T.; Kubo, J.; Mondragon, M.; Zoupanos, G.

1999-01-01

All-loop Finite Unified Theories (FUTs) are very interesting N=1 GUTs in which a complete reduction of couplings has been achieved. FUTs realize an old field theoretical dream and have remarkable predictive power. Reduction of dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exists RGI relations among dimensionless couplings that guarantee the vanishing of the β- functions in certain N=1 supersymmetric GUTS even to all orders. Recent developments in the soft supersymmetry breaking (SSB) sector of N=1 GUTs and FUTs lead to exact RGI relations also in this sector of the theories. Of particular interest is a RGI sum rule for the soft scalar masses holding to all orders. The characteristic features of SU(5) models that have been constructed based on the above tools are: a) the old agreement of the top quark prediction with the measured value remains unchanged, b) the lightest Higgs boson is predicted to be around 120 GeV, c) the s-spectrum starts above several hundreds of GeV

Scaling algebras and renormalization group in algebraic quantum field theory

International Nuclear Information System (INIS)

Buchholz, D.; Verch, R.

1995-01-01

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined. (orig.)

Tracing the string: BMN correspondence at finite J2/N

International Nuclear Information System (INIS)

Pearson, John; Vaman, Diana; Verlinde, Herman; Volovich, Anastasia; Spradlin, Marcus

2003-01-01

Employing the string bit formalism of hep-th/0209215, we identify the basis transformation that relates BMN operators in N=4 gauge theory to string states in the dual string field theory at finite g 2 =J 2 /N. In this basis, the supercharge truncates at linear order in g 2 , and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of hep-th/0206073 for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g 2 2 contact term in the string bit Hamiltonian. The resulting leading order mass renormalization of string states agrees with the recently computed shift in conformal dimension of BMN operators in the gauge theory. (author)

Spin-orbit interaction and asymmetry effects on Kondo ridges at finite magnetic field

DEFF Research Database (Denmark)

Grap, Stephan; Andergassen, Sabine; Paaske, Jens

2011-01-01

ridges, which are robust against SOI as time-reversal symmetry is preserved. As a result of the crossing of a spin-up and a spin-down level at vanishing SOI, two additional Kondo plateaus appear at finite B. They are not protected by symmetry and rapidly vanish if the SOI is turned on. Left......-right asymmetric level-lead couplings and detuned on-site energies lead to a simultaneous breaking of left-right and bonding-antibonding state symmetry. In this case, the finite-B Kondo ridges in the Vg-B plane are bent with respect to the Vg axis. For the Kondo ridge to develop, different level renormalizations......We study electron transport through a serial double quantum dot with Rashba spin-orbit interaction (SOI) and Zeeman field of amplitude B in the presence of local Coulomb repulsion. The linear conductance as a function of a gate voltage Vg equally shifting the levels on both dots shows two B=0 Kondo...

Amount of gauge transformations in neutral-vector field theory. [Renormalization, free Lagrangian density

Energy Technology Data Exchange (ETDEWEB)

Kubo, R; Yokoyama, K

1974-11-01

The purpose of this work is to study the structure of c-number gauge transformation in connection with renormalization problem. In the wide theory of neutral vector fields, there is the gauge structure described essentially by free Lagrangian density. The c-number gauge transformation makes the Lagrangian invariant correspondingly to the usual case of quantum electrodynamics. The c-number transformation can be used to derive relationships among all relevant renormalization constants in the case of interacting fields. In the presence of interaction, total Lagrangian density L is written as L=L/sub 0/+L/sub 1/+L/sub 2/, where L/sub 1/ is given from matter-field Lagrangian density, and L/sub 2/ denotes necessary additional counter terms. In order to conserve the gauge structure, the form of L is invariant under the gauge transformation. Since L matter is self-adjoining, L/sub 1/ remains invariant by itself under the transformation. The form of L/sub 2/ is finally given from the observation that L/sub 3/ cannot contain wave-function renormalization constants. Since L/sub 2/ is invariant under q-number gauge transformation, this transformation in unrenormalized form makes the present L form-invariant. Therefore, together with the above results, auxiliary fields produce the q-number gauge transformation for renormalized fields.

Renormalization of Extended QCD2

International Nuclear Information System (INIS)

Fukaya, Hidenori; Yamamura, Ryo

2015-01-01

Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N c , to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region

The quantum-field renormalization group in the problem of a growing phase boundary

International Nuclear Information System (INIS)

Antonov, N.V.; Vasil'ev, A.N.

1995-01-01

Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik's assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants (open-quotes chargeclose quotes). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundary and time, δ h and δ t , which satisfy the exact relationship 2 δ h = δ t + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab

NSVZ scheme with the higher derivative regularization for N=1 SQED

International Nuclear Information System (INIS)

Kataev, A.L.; Stepanyantz, K.V.

2013-01-01

The exact NSVZ relation between a β-function of N=1 SQED and an anomalous dimension of the matter superfields is studied within the Slavnov higher derivative regularization approach. It is shown that if the renormalization group functions are defined in terms of the bare coupling constant, this relation is always valid. In the renormalized theory the NSVZ relation is obtained in the momentum subtraction scheme supplemented by a special finite renormalization. Unlike the dimensional reduction, the higher derivative regularization allows to fix this finite renormalization. This is made by imposing the conditions Z 3 (α,μ=Λ)=1 and Z(α,μ=Λ)=1 on the renormalization constants of N=1 SQED, where Λ is a parameter in the higher derivative term. The results are verified by the explicit three-loop calculation. In this approximation we relate the DR ¯ scheme and the NSVZ scheme defined within the higher derivative approach by the finite renormalization

Metastability of the ({phi}{sub i}{phi}{sub i}){sub 3}{sup 2} model at finite temperature and density

Energy Technology Data Exchange (ETDEWEB)

Ananos, G.N.J.; Malbouisson, A.P.C.; Svaiter, N.F.

1996-11-01

Using concurrently the dimensional and analytic regularization methods we applied the Gross-Neveu model at finite temperature and density (chemical potential) in a D-dimensional spacetime. The renormalized effective potential is presented at the one-loop approximation. In the case of non-zero chemical potential we show that the effective potential acquires an imaginary part, which means that the system becomes metastable, indicating the possibility of a first phase transition. (author). 13 refs.; e-mail: nfuxsvai at lca1.drp.cbpf.br.

Computing the effective action with the functional renormalization group

Energy Technology Data Exchange (ETDEWEB)

Codello, Alessandro [CP3-Origins and the Danish IAS University of Southern Denmark, Odense (Denmark); Percacci, Roberto [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Rachwal, Leslaw [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Tonero, Alberto [ICTP-SAIFR and IFT, Sao Paulo (Brazil)

2016-04-15

The ''exact'' or ''functional'' renormalization group equation describes the renormalization group flow of the effective average action Γ{sub k}. The ordinary effective action Γ{sub 0} can be obtained by integrating the flow equation from an ultraviolet scale k = Λ down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. (orig.)

Renormalization of gauge theories

International Nuclear Information System (INIS)

Becchi, C.; Rouet, A.; Stora, R.

1975-04-01

Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts. These identities are proved to all orders of renormalized perturbation theory, within the BPHZ framework, when the underlying Lie algebra is semi-simple and the gauge function is chosen to be linear in the fields in such a way that all fields are massive. An example, the SU2 Higgs Kibble model is analyzed in detail: the asymptotic theory is formulated in the perturbative sense, and shown to be reasonable, namely, the physical S operator is unitary and independant from the parameters which define the gauge function [fr

Absence of renormalization group pathologies near the critical temperature. Two examples

International Nuclear Information System (INIS)

Haller, K.; Kennedy, T.

1996-01-01

We consider real-space renormalization group transformations for Ising-type systems which are formally defined by where T(σ, σ') is a probability kernel, i.e., Σ σ' T(σ, σ') = 1, for every configuration σ. For each choice of the block spin configuration σ', let μ σ' , be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional to T(σ, σ') exp[ -H(σ)]. We give a condition which is sufficient to imply that the renormalized Hamiltonian H' is defined. Roughly speaking, the condition is that the collection of measures μ σ' is in the high-temperature phase uniformly in the block spin configuration σ'. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacing b = 2 on the square lattice with β c and the Kadanoff transformation with parameter p on the triangular lattice in a subset of the β, p plane that includes values of β greater than β c

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

Science.gov (United States)

Rose, F.; Dupuis, N.

2018-05-01

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.

Renormalization-group-invariant 1/N corrections to nontrival φ4 theory

International Nuclear Information System (INIS)

Smekal, L.v.; Langfeld, K.; Reinhardt, H.; Langbein, R.F.

1994-01-01

In the framework of path integral linearization techniques, the effective potential and the master field equation for massless φ 4 theory, in the modified loop expansion around the mean field, are derived up to next to leading order. In the O(N)-symmetric theory, these equations are equivalent to a subsummation of O(N) and order 1 diagrams. A renormalization prescription is proposed which is manifestly renormalization group invariant. The numerical results for the potential in next to leading order agree qualitatively well with the leading order ones. In particular, the nontrivial phase structure remains unchanged. Quantitatively, the corrections ar small for N much-gt 8, but even for N as small as one their essential effect is to modify the scaling coefficient β 0 in the Callan-Symanzik β function, in accordance with conventional loop expansions. The numerical results are best parametrized by scaling improved mean field formulas. Dimensional transmutation renders the overall (physical) mass scale M 0 , generated by a dynamical breaking of scale invariance, the only adjustable parameter of the theory. Renormalization group invariance of the numerical results is explicitly verified

Full counting statistics of level renormalization in electron transport through double quantum dots

International Nuclear Information System (INIS)

Luo Junyan; Shen Yu; Cen Gang; He Xiaoling; Wang Changrong; Jiao Hujun

2011-01-01

We examine the full counting statistics of electron transport through double quantum dots coupled in series, with particular attention being paid to the unique features originating from level renormalization. It is clearly illustrated that the energy renormalization gives rise to a dynamic charge blockade mechanism, which eventually results in super-Poissonian noise. Coupling of the double dots to an external heat bath leads to dephasing and relaxation mechanisms, which are demonstrated to suppress the noise in a unique way.

RENORMALIZATION FACTOR AND ODD-OMEGA GAP SINGLET SUPERCONDUCTIVITY

NARCIS (Netherlands)

DOLGOV, OV; LOSYAKOV, VV

1994-01-01

Abrahams et al. [Phys. Rev. B 47 (1993) 513] have considered the possibility of a nonzero critical temperature of the superconductor transition to the state with odd-omega pp function and shown that the condition for it is the following inequality for the renormalization factor. Z (k, omega(n)) <1.

Renormalization in charged colloids: non-monotonic behaviour with the surface charge

International Nuclear Information System (INIS)

Haro-Perez, C; Quesada-Perez, M; Callejas-Fernandez, J; Schurtenberger, P; Hidalgo-Alvarez, R

2006-01-01

The static structure factor S(q) is measured for a set of deionized latex dispersions with different numbers of ionizable surface groups per particle and similar diameters. For a given volume fraction, the height of the main peak of S(q), which is a direct measure of the spatial ordering of latex particles, does not increase monotonically with the number of ionizable groups. This behaviour cannot be described using the classical renormalization scheme based on the cell model. We analyse our experimental data using a renormalization model based on the jellium approximation, which predicts the weakening of the spatial order for moderate and large particle charges. (letter to the editor)

Renormalization of supersymmetric gauge theories on orbifolds: Brane gauge couplings and higher derivative operators

International Nuclear Information System (INIS)

Groot Nibbelink, Stefan; Hillenbach, Mark

2005-01-01

We consider supersymmetric gauge theories coupled to hypermultiplets on five- and six-dimensional orbifolds and determine the bulk and local fixed point renormalizations of the gauge couplings. We infer from a component analysis that the hypermultiplet does not induce renormalization of the brane gauge couplings on the five-dimensional orbifold S 1 /Z 2 . This is not due to supersymmetry, since the bosonic and fermionic contributions cancel separately. We extend this investigation to T 2 /Z N orbifolds using supergraph techniques in six dimensions. On general Z N orbifolds the gauge couplings do renormalize at the fixed points, except for the Z 2 fixed points of even ordered orbifolds. To cancel the bulk one-loop divergences a dimension six higher derivative operator is needed, in addition to the standard bulk gauge kinetic term.

Renormalization of spin excitations in hexagonal HoMnO3 by magnon-phonon coupling

Science.gov (United States)

Kim, Taehun; Leiner, Jonathan C.; Park, Kisoo; Oh, Joosung; Sim, Hasung; Iida, Kazuki; Kamazawa, Kazuya; Park, Je-Geun

2018-05-01

Hexagonal HoMnO3, a two-dimensional Heisenberg antiferromagnet, has been studied via inelastic neutron scattering. A simple Heisenberg model with a single-ion anisotropy describes most features of the spin-wave dispersion curves. However, there is shown to be a renormalization of the magnon energies located at around 11 meV. Since both the magnon-magnon interaction and magnon-phonon coupling can affect the renormalization in a noncollinear magnet, we have accounted for both of these couplings by using a Heisenberg XXZ model with 1 /S expansions [1] and the Einstein site phonon model [13], respectively. This quantitative analysis leads to the conclusion that the renormalization effect primarily originates from the magnon-phonon coupling, while the spontaneous magnon decay due to the magnon-magnon interaction is suppressed by strong two-ion anisotropy.

Pade expansion and the renormalization of nucleon-nucleon scattering

International Nuclear Information System (INIS)

Yang Jifeng; Huang Jianhua; Liu Dan

2006-01-01

The importance of imposing physical boundary conditions on the T-matrix to remove to nonperturbative renormalization prescription dependence is stressed and demonstrated in two diagonal channels 1 P 1 and 1 D 2 , with the help of Pade expansion. (authors)

Propagators and renormalization transformations for lattice gauge theories. Pt. 2

International Nuclear Information System (INIS)

Balaban, T.

1984-01-01

We continue the studies of the Paper I and extend the results of this paper to operators defined by restrictions on different scales, or by renormalization transformations of different orders. (orig.)

Perfect 3-dimensional lattice actions for 4-dimensional quantum field theories at finite temperature

International Nuclear Information System (INIS)

Kerres, U.; Mack, G.; Palma, G.

1994-12-01

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bololiubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for φ 4 -theory and scalar electrodynamics. The Balaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here. (orig.)

Quasi-renormalization of the axial vector model

International Nuclear Information System (INIS)

Schweda, M.

1979-01-01

Using the regulator-free BPHZL renormalization scheme the problem of anomalies in a massive axial vector meson model is reinvestigated. The Adler-Bardeen-Bell-Jackiw anomaly introduces some impressive modifications: the nontrivial self-energy and the counterterm of the longitudinal part of the axial vector field depend on the anomaly via the anomalous Ward identity. The investigations are based on a Fermi-type gauge. (author)

Quarkonia from charmonium and renormalization group equations

International Nuclear Information System (INIS)

Ditsas, P.; McDougall, N.A.; Moorhouse, R.G.

1978-01-01

A prediction of the upsilon and strangeonium spectra is made from the charmonium spectrum by solving the Salpeter equation using an identical potential to that used in charmonium. Effective quark masses and coupling parameters αsub(s) are functions of the inter-quark distance according to the renormalization group equations. The use of the Fermi-Breit Hamiltonian for obtaining the charmonium hyperfine splitting is criticized. (Auth.)

Applications of the renormalization group approach to problems in quantum field theory

International Nuclear Information System (INIS)

Renken, R.L.

1985-01-01

The presence of fluctuations at many scales of length complicates theories of quantum fields. However, interest is often focused on the low-energy consequences of a theory rather than the short distance fluctuations. In the renormalization-group approach, one takes advantage of this by constructing an effective theory with identical low-energy behavior, but without short distance fluctuations. Three problems of this type are studied here. In chapter 1, an effective lagrangian is used to compute the low-energy consequences of theories of technicolor. Corrections to weak-interaction parameters are found to be small, but conceivably measurable. In chapter 2, the renormalization group approach is applied to second order phase transitions in lattice gauge theories such as the deconfining transition in the U(1) theory. A practical procedure for studying the critical behavior based on Monte Carlo renormalization group methods is described in detail; no numerical results are presented. Chapter 3 addresses the problem of computing the low-energy behavior of atoms directly from Schrodinger's equation. A straightforward approach is described, but is found to be impractical

Renormalization of gauge fields models

International Nuclear Information System (INIS)

Becchi, C.; Rouet, A.; Stora, R.

1974-01-01

A new approach to gauge field models is described. It is based on the Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme making extensive use of the quantum action principle, and the Slavnov invariance. The quantum action principle being first summarized in the framework of the BPHZ is then applied to a global symmetry problem. The symmetry property of the gauge field Lagrangians in the tree approximation is exhibited, and the preservation of this property at the quantum level is discussed. The main results relative to the Abelian and SU(2) Higgs-Kibble models are briefly reviewed [fr

Renormalization of the scalar field theory with spontaneously broken discrete symmetry without shifting the field vacuum expectation value

International Nuclear Information System (INIS)

Solin, J.

1988-01-01

The one-loop renormalization of the λφ 4 theory with a spontaneous breaking of its discrete (reflection) symmetry is analyzed. It is explicitly shown that it is not necessary to forcefully eliminate the linear counterterm in the shifted field (accomplished usually by shifting the vacuum expectation value of the field) in order to have the renormalized Lagrangian still formally invariant under the original discrete symmetry. It is further shown, using the normal-ordering procedure, that the renormalization carried out in the customary form completely wipes out the tadpole diagram contributions from the original Lagrangian. As a consequence, the same renormalized Lagrangian can be also obtained from the original bare Lagrangian which, however, has been normal-ordered and as such cannot cause the linear counterterm in the shifted field since now the tadpole diagrams are absent altogether. These analyses should support the view that the vacuum expectation value of the field is of a group-theoretical origin rather than a field-theoretical origin, and as such should not change independently of the shifted field in the course of renormalization

The evolution of Bogolyubov's renormalization group

International Nuclear Information System (INIS)

Shirkov, D.V.

2000-01-01

We review the evolution of the concept of Renormalization Group (RG). This notion, as was first introduced in quantum field theory (QFT) in the mid-fifties in N.N.Bogolyubov's formulation, is based upon a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of a boundary condition) specifying some particular solution. To illustrate this approach's effectiveness, we end with its application to the analysis of the laser beam self-focusing in a non-linear medium

The renormalized action principle in quantum field theory

International Nuclear Information System (INIS)

Balasin, H.

1990-03-01

The renormalized action principle holds a central position in field theory, since it offers a variety of applications. The main concern of this work is the proof of the action principle within the so-called BPHZ-scheme of renormalization. Following the classical proof given by Lam and Lowenstein, some loopholes are detected and closed. The second part of the work deals with the application of the action principle to pure Yang-Mills-theories within the axial gauge (n 2 ≠ 0). With the help of the action principle we investigate the decoupling of the Faddeev-Popov-ghost-fields from the gauge field. The consistency of this procedure, suggested by three-graph approximation, is proven to survive quantization. Finally we deal with the breaking of Lorentz-symmetry caused by the presence of the gauge-direction n. Using BRST-like techniques and the semi-simplicity of the Lorentz-group, it is shown that no new breakings arise from quantization. Again the main step of the proof is provided by the action principle. (Author, shortened by G.Q.)

Renormalization effects and phonon density of states in high temperature superconductors

Directory of Open Access Journals (Sweden)

Vinod Ashokan

2013-02-01

Full Text Available Using the versatile double time thermodynamic Green's function approach based on many body theory the renormalized frequencies, phonon energy line widths, shifts and phonon density of states (PDOS are investigated via a newly formulated Hamiltonian (does not include BCS type Hamiltonian that includes the effects of electron-phonon, anharmonicities and that of isotopic impurities. The automatic appearance of pairons, temperature, impurity and electron-phonon coupling of renormalized frequencies, widths, shifts and PDOS emerges as a characteristic feature of present theory. The numerical investigations on PDOS for the YBa2Cu3O7 − δ crystal predicts several new feature of high temperature superconductors (HTS and agreements with experimental observations.

The Bogolyubov renormalization group. Second English printing

International Nuclear Information System (INIS)

Shirkov, D.V.

1996-01-01

We begin with personal notes describing the atmosphere of 'Bogolyubov renormalization group' birth. Then we expose the history of RG discovery in the QFT and of the RG method devising in the mid-fifties. The third part is devoted to proliferation of RG ideas into diverse parts of theoretical physics. We conclude with discussing the perspective of RG method further development and its application in mathematical physics. 58 refs

Renormalization of total sets of states into generalized bases with a resolution of the identity

International Nuclear Information System (INIS)

Vourdas, A

2017-01-01

A total set of states for which we have no resolution of the identity (a ‘pre-basis’), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes them a ‘generalized basis’, which is practically useful. The dresssing mechanism is inspired by Shapley’s methodology in cooperative game theory, and it uses Möbius transforms. There is non-independence and redundancy in these generalized bases, which is quantified with a Shannon type of entropy. Due to this redundancy, calculations based on generalized bases are sensitive to physical changes and robust in the presence of noise. For example, the representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in the coefficients. Also in a physical system with a ground state which changes abruptly at some value of the coupling constant, the proposed methodology detects such changes, even when noise is added to the parameters in the Hamiltonian of the system. (paper)

Functional renormalization-group approach to the Pokrovsky-Talapov model via the modified massive Thirring fermions

Science.gov (United States)

Nosov, P. A.; Kishine, Jun-ichiro; Ovchinnikov, A. S.; Proskurin, I.

2017-12-01

We consider a possibility of the topological Kosterlitz-Thouless (KT) transition in the two-dimensional Pokrovsky-Talapov model with a finite misfit parameter and discuss its relevance to the theory of critical behavior in thin films of monoaxial chiral helimagnets. For this purpose, the initial model is reformulated in terms of the two-dimensional relativistic model of massive Thirring fermions and the Wetterich's functional renormalization-group (RG) approach is employed. In the new formalism, the misfit parameter corresponds to an effective gauge field that can be included in the RG scheme on an equal footing with the other parameters of the theory. Our main result is that the presence of the misfit parameter, which may be attributed to the Dzyaloshinskii-Moriya interaction in the magnetic system, rules out the KT transition. To support this finding, we provide an additional intuitive explanation of the KT scenario breakdown by using the mapping onto the Coulomb gas model. In the framework of the model, the misfit parameter has a meaning of an effective in-plane electric field that prevents a formation of bound vortex-antivortex pairs.

On Newton-Cartan local renormalization group and anomalies

Energy Technology Data Exchange (ETDEWEB)

Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); INFN Sezione di Perugia,Via A. Pascoli, 06123 Perugia (Italy); Baiguera, Stefano; Filippini, Francesco [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); TIFPA - INFN, c/o Dipartimento di Fisica, Università di Trento,38123 Povo (Italy)

2016-11-28

Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.

On Newton-Cartan local renormalization group and anomalies

International Nuclear Information System (INIS)

Auzzi, Roberto; Baiguera, Stefano; Filippini, Francesco; Nardelli, Giuseppe

2016-01-01

Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.

Comment on non-renormalization theorem in the four dimensional superstrings

International Nuclear Information System (INIS)

Soda, Jiro; Nakazawa, Naohito; Sakai, Kenji; Ojima, Shuichi.

1987-10-01

We discuss non-renormalization theorem in the context of the four dimensional superstrings. We explicitly demonstrate that the graviton 3-point one-loop amplitude does not vanish in contrast to the ten dimensional superstring theories. (author)

Dynamic mass generation and renormalizations in quantum field theories

International Nuclear Information System (INIS)

Miransky, V.A.

1979-01-01

It is shown that the dynamic mass generation can destroy the multiplicative renormalization relations and lead to new type divergences in the massive phase. To remove these divergences the values of the bare coupling constants must be fixed. The phase diagrams of gauge theories are discussed

Updated RENORM/MBR Predictions for Diffraction at the LHC

CERN Document Server

Goulianos, K

2015-01-01

Updated RENORM/MBR-model predictions of diffractive, total, and total-inelastic cross sections at the LHC are presented and compared with experimental results and predictions from other models. In addition, expectations for diffraction at the upcoming LHC run at √s = 13 TeV are discussed.

Quantitative determination of spin-dependent quasiparticle renormalization in ferromagnetic 3d metals

Energy Technology Data Exchange (ETDEWEB)

Sanchez-Barriga, Jaime; Varykhalov, Andrei; Fink, Joerg; Rader, Oliver; Duerr, Hermann; Eberhardt, Wolfgang [Bessy GmbH, Berlin (Germany)

2008-07-01

Spin dependent low-energy electronic excitations in 3d ferromagnets are of special interest due to the need of a microscopic understanding of the electronic structure of solids. Low-energy electrons (or holes) become dressed by a cloud of excitations resulting in quasiparticles of a finite lifetime and a different effective mass. These type of excitations have been studied by many theoretical methods, and it has been found that because of many body effects no sharp quasiparticle peaks exist for binding energies larger than 2 eV. Interestingly, it has been shown that strong correlation effects could particularly affect majority spin electrons, leading to a pronounced damping of quasiparticles at binding energies around 2 eV and above. In order to give an experimental corroboration to these findings, we have performed a systematic study of the spin-dependent quasiparticle lifetime and band structure of ferromagnetic 3d transition metal surfaces by means of spin and angle-resolved photoemission spectroscopy. On hcp Co(0001), fcc Ni(111) and bcc Fe(110), we have found a more pronounced renormalization of the majority spin quasiparticle spectral weight going from Ni to Co which are both strong ferromagnets. For Fe, a weak ferromagnet, such a process becomes more prominent in the minority channel.

Finite field equation for asymptotically free phi4 theory

International Nuclear Information System (INIS)

Brandt, R.A.; Wing-chiu, N.; Wai-Bong, Y.

1979-01-01

We consider the finite local field equation - (D 7 Alembertian + m 2 ) phi (x) = lim/sub xitsarrow-rightts/0[1/6gZ (xi 2 ):phi (x - xi) phi (x) phi (x + xi):- Δ (xi 2 ) phi (x) + sigma (xi 2 )(xi x partial/sub x/) 2 phi (x)], which rigorously describes gphi 4 scalar field theory, and the operator-product expansion phi (xi) phi (0) /sup approximately/ /sub xitsarrow-rightts0/F (xi 2 ) N[phi 2 ], where N[phi 2 ] denotes a normal product. For g 2 ), Δ (xi 2 ), sigma (xi 2 ), and F (xi 2 ). We perform the R transformation phi (x) → phi (x) + r on the finite field equation and obtain the operator part of the change to be proportional to lim/sub xitsarrow-rightts0/Z (xi 2 ) F (xi 2 ) N[phi 2 ] which vanishes by our knowledge of the functions Z (xi 2 ) and F (xi 2 ). We have therefore verified rigorously the partial R invariance of - vertical-bargvertical-barphi 4 theory. We discuss and solve the technical problem of finding the solution for renormalization-group equations with a matrix γ function where the lowest-order expansions of the various elements do not begin with the same powers of g

Renormalization group and relations between scattering amplitudes in a theory with different mass scales

International Nuclear Information System (INIS)

Gulov, A.V.; Skalozub, V.V.

2000-01-01

In the Yukawa model with two different mass scales the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. Considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives possibility to reduce the problem to the scattering of light particles on the external field substituting a heavy virtual state. Applications of the results to problem of searching new physics beyond the Standard Model are discussed [ru

A real-space renormalization approach to the Kubo-Greenwood formula in mirror Fibonacci systems

International Nuclear Information System (INIS)

Sanchez, Vicenta; Wang Chumin

2006-01-01

An exact real-space renormalization method is developed to address the electronic transport in mirror Fibonacci chains at a macroscopic scale by means of the Kubo-Greenwood formula. The results show that the mirror symmetry induces a large number of transparent states in the dc conductivity spectra, contrary to the simple Fibonacci case. A length scaling analysis over ten orders of magnitude reveals the existence of critically localized states and their ac conduction spectra show a highly oscillating behaviour. For multidimensional quasiperiodic systems, a novel renormalization plus convolution method is proposed. This combined renormalization + convolution method has shown an extremely elevated computing efficiency, being able to calculate electrical conductance of a three-dimensional non-crystalline solid with 10 30 atoms. Finally, the dc and ac conductances of mirror Fibonacci nanowires are also investigated, where a quantized dc-conductance variation with the Fermi energy is found, as observed in gold nanowires

A General Finite Element Scheme for Limit State Analysis and Optimization

DEFF Research Database (Denmark)

Damkilde, Lars

1999-01-01

Limit State analysis which is based on a perfect material behaviour is used in many different applications primarily within Structural Engineering and Geotechnics. The calculation methods have not reached the same level of automation such as Finite Element Analysis for elastic structures....... The computer based systems are more ad hoc based and are typically not well-integrated with pre- and postprocessors well-known from commercial Finite Element codes.A finite element based formulation of limit state analysis is presented which allows an easy integration with standard Finite Element codes...... for elastic analysis. In this way the user is able to perform a limit state analysis on the same model used for elastic analysis only adding data for the yield surface.The method is based on the lower-bound theorem and uses stress-based elements with a linearized yield surface. The mathematical problem...

Zero-temperature renormalization of the 2D transverse Ising model

International Nuclear Information System (INIS)

Kamieniarz, G.

1982-08-01

A zero-temperature real-space renormalization-group method is applied to the transverse Ising model on planar hexagonal, triangular and quadratic lattices. The critical fields and the critical exponents describing low-field large-field transition are calculated. (author)

Renormalization and operator product expansion in theories with massless particles

International Nuclear Information System (INIS)

Anikin, S.A.; Smirnov, V.A.

1985-01-01

Renormalization procedure in theories including massless particles is presented. With the help of counterterm formalism the operator product expansion for arbitrary composite fields is derived. The coefficient functions are explicitly expressed in terms of certain Green's functions. (author)

Conductance of finite systems and scaling in localization theory

Science.gov (United States)

Suslov, I. M.

2012-11-01

The conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)). Usually it is defined by the Landauer-type formulas, which remain open the following questions: (a) exclusion of the contact resistance in the many-channel case; (b) correspondence of the Landauer conductance with internal properties of the system; (c) relation with the diffusion coefficient D(ω, q) of an infinite system. The answers to these questions are obtained below in the framework of two approaches: (1) self-consistent theory of localization by Vollhardt and Wölfle, and (2) quantum mechanical analysis based on the shell model. Both approaches lead to the same definition for the conductance of a finite system, closely related to the Thouless definition. In the framework of the self-consistent theory, the relations of finite-size scaling are derived and the Gell-Mann-Low functions β( g) for space dimensions d = 1, 2, 3 are calculated. In contrast to the previous attempt by Vollhardt and Wölfle (1982), the metallic and localized phase are considered from the same standpoint, and the conductance of a finite system has no singularity at the critical point. In the 2D case, the expansion of β( g) in 1/ g coincides with results of the σ-model approach on the two-loop level and depends on the renormalization scheme in higher loops; the use of dimensional regularization for transition to dimension d = 2 + ɛ looks incompatible with the physical essence of the problem. The results are compared with numerical and physical experiments. A situation in higher dimensions and the conditions for observation of the localization law σ(ω) ∝ - iω for conductivity are discussed.

Conductance of finite systems and scaling in localization theory

International Nuclear Information System (INIS)

Suslov, I. M.

2012-01-01

The conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)). Usually it is defined by the Landauer-type formulas, which remain open the following questions: (a) exclusion of the contact resistance in the many-channel case; (b) correspondence of the Landauer conductance with internal properties of the system; (c) relation with the diffusion coefficient D(ω, q) of an infinite system. The answers to these questions are obtained below in the framework of two approaches: (1) self-consistent theory of localization by Vollhardt and Wölfle, and (2) quantum mechanical analysis based on the shell model. Both approaches lead to the same definition for the conductance of a finite system, closely related to the Thouless definition. In the framework of the self-consistent theory, the relations of finite-size scaling are derived and the Gell-Mann-Low functions β(g) for space dimensions d = 1, 2, 3 are calculated. In contrast to the previous attempt by Vollhardt and Wölfle (1982), the metallic and localized phase are considered from the same standpoint, and the conductance of a finite system has no singularity at the critical point. In the 2D case, the expansion of β(g) in 1/g coincides with results of the σ-model approach on the two-loop level and depends on the renormalization scheme in higher loops; the use of dimensional regularization for transition to dimension d = 2 + ε looks incompatible with the physical essence of the problem. The results are compared with numerical and physical experiments. A situation in higher dimensions and the conditions for observation of the localization law σ(ω) ∝ −iω for conductivity are discussed.

Ultrasoft renormalization of the potentials in vNRQCD

Energy Technology Data Exchange (ETDEWEB)

Stahlhofen, Maximilian Horst

2009-02-18

The effective field theory vNRQCD allows to describe among others the production of top-antitop pairs in electron-positron collisions at threshold, i.e. with very small relative velocity {upsilon} << 1 of the quarks. Potentially large logarithms {proportional_to} ln {upsilon} are systematically summed up and lead to a scale dependence of the Wilson coefficients of the theory. The missing contributions to the cross section {sigma}(e{sup +}e{sup -} {yields} t anti t) in the resonance region at NNLL level are the so-called mixing contributions to the NNLL anomalous dimension of the S-wave production/annihilation current of the topquark pair. To calculate these one has to know the NLL renormalization group running of so-called potentials (4-quark operators). The dominant contributions to the anomalous dimension of these potentials come from vNRQCD diagrams with ultrasoft gluon loops. The aim of this thesis is to derive the complete ultrasoft NLL running of the relevant potentials. For that purpose the UV divergent parts of about 10{sup 4} two-loop diagrams are determined. Technical and conceptional issues are discussed. Some open questions related to the calculation of the non-Abelian two-loop diagrams arise. Preliminary results are analysed with regard to the consequences for the mentioned cross section and its theoretical uncertainty. (orig.)

Zero Point Energy of Renormalized Wilson Loops

OpenAIRE

Hidaka, Yoshimasa; Pisarski, Robert D.

2009-01-01

The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero wh...

A renormalization group theory of cultural evolution

OpenAIRE

Fath, Gabor; Sarvary, Miklos

2003-01-01

We present a theory of cultural evolution based upon a renormalization group scheme. We consider rational but cognitively limited agents who optimize their decision making process by iteratively updating and refining the mental representation of their natural and social environment. These representations are built around the most important degrees of freedom of their world. Cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequa...

Renormalization of the Sine-Gordon model and nonconservation of the kink current

International Nuclear Information System (INIS)

Huang, K.; Polonyi, J.

1991-01-01

The authors of this paper renormalize the (1 + 1)-dimensional sine-Gordon model by placing it on a Euclidean lattice, and study the renormalization group flow. The authors start with a compactified theory with controllable vortex activity. In the continuum limit the theory has a phase in which the kink current is anomalous, with divergence given by the vortex density. The phase structure is quite complicated. Roughly speaking, the system is normal for small coupling T. At the Kosterlitz-Thouless point T = π/2, the current can become anomalous. At the Coleman point T = 8π either the current becomes anomalous or the theory becomes trivial

Functional renormalization group and Kohn-Sham scheme in density functional theory

Science.gov (United States)

Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo

2018-04-01

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

Renormalization group scale-setting from the action—a road to modified gravity theories

International Nuclear Information System (INIS)

Domazet, Silvije; Štefančić, Hrvoje

2012-01-01

The renormalization group (RG) corrected gravitational action in Einstein–Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein–Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein–Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor. (paper)

Renormalization group scale-setting from the action—a road to modified gravity theories

Science.gov (United States)

Domazet, Silvije; Štefančić, Hrvoje

2012-12-01

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor.

Finite-State Complexity and the Size of Transducers

Directory of Open Access Journals (Sweden)

Cristian Calude

2010-08-01

Full Text Available Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our main result, we show that the state-size hierarchy with respect to a standard encoding is infinite. We consider also hierarchies yielded by more general computable encodings.

Critical endline of the finite temperature phase transition for 2+1 flavor QCD away from the SU(3-flavor symmetric point

Directory of Open Access Journals (Sweden)

Nakamura Yoshifumi

2018-01-01

Full Text Available We investigate the critical end line of the finite temperature phase transition of QCD away from the SU(3-flavor symmetric point at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and non-perturbatively O(a- improved Wilson-clover fermion action. The critical end line is determined by using the intersection point of kurtosis, employing the multi-parameter, multi-ensemble reweighting method at the temporal size NT = 6 and lattice spacing as low as a ≈0.19 fm.

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.

Self-energies, renormalization factor, Luttinger sum rule and quasiparticle structure of the Hubbard systems

International Nuclear Information System (INIS)

Lopez-Aguilar, F.; Costa-Quintana, J.

1992-01-01

In this paper, the authors give a method for obtaining the renormalized electronic structure of the Hubbard systems. The first step is the determination of the self-energy beyond the Hartree-Fock approximation. This self-energy is constructed from several dielectric response functions. The second step is the determination of the quasiparticle band structure calculation which is performed from an appropriate modification of the augmented plane wave method. The third step consists in the determination of the renormalized density of states deduced from the spectral functions. The analysis of the renormalized density of states of the strongly correlated systems leads to the conclusion that there exist three types of resonances in their electronic structures, the lower energy resonances (LER), the middle energy resonances (MER) and the upper energy resonances (UER). In addition, the authors analyze the conditions for which the Luttinger theorem is satisfied. All of these questions are determined in a characteristic example which allows to test the theoretical method

Two-and three-dimension Potts magnetism in the renormalization group approximation

International Nuclear Information System (INIS)

Silva, L.R. da.

1985-01-01

Through a real space Renormalization Group (RG) technique we discuss the criticality of various physical systems, calculate order parameters for geometrical problems and analyse convergence aspects of the RG theory. (author) [pt

Renormalization group equations with multiple coupling constants

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1975-01-01

The main purpose of this paper is to study the renormalization group equations of a renormalizable field theory with multiple coupling constants. A method for the investigation of the asymptotic stability is presented. This method is applied to a gauge theory with Yukawa and self-quartic couplings of scalar mesons in order to find the domains of asymptotic freedom. An asymptotic expansion for the solutions which tend to the origin of the coupling constants is given

Periodically driven random quantum spin chains: real-space renormalization for Floquet localized phases

Science.gov (United States)

Monthus, Cécile

2017-07-01

When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding strong disorder renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.

The renormalization of collective states and the improper initial or final states in NFT

International Nuclear Information System (INIS)

Bes, D.R.; Dussel, G.G.; Perazzo, R.P.J.; Sofia, H.M.

1978-01-01

The collective lines in a given diagram are renormalized by including higher order processes. The problem is cast into the form of a conventional linear algebraic matrix equation that allows a simple treatment of the normalization conditions. It is shown that the states entering in the renormalization of the phonons become improper initial or final states, if dressed phonons are used in the intermediate states. A simple extension of this argument allows one to justify one of the rules given in the formulation of the NFT. (Auth.)

On the nucleon renormalization in many nucleon problems due to pionic degrees of freedom

International Nuclear Information System (INIS)

Sauer, P.U.; Sawicki, M.; Furui, Sadataka.

1985-01-01

Conceptual problems of unified two-nucleon force models are discussed. The force models are based on the pion-nucleon vertex and attempt a description of the nucleon-nucleon interaction below and above pion threshold. The conceptual problems arise from the nucleon renormalization due to pionic degrees of freedom. Keeping channels with a single pion only no renormalization procedure can be given which is consistent in the one-nucleon and in the many-nucleon systems. The medium dependence of the one-pion exchange potential is illustrated. (author)

Investigation of the role of the rho-meson exchange in spin-isospin strength distribution effects in a finite nucleus

International Nuclear Information System (INIS)

Cohen, J.

1984-01-01

We present a unified study of the role of the rho-exchange interaction in spin-isospin strength distribution effects in a finite nuclear system. We study both the longitudinal (sigma-arrow-rightxqtau/sub lambda/, where q is the momentum transfer to the nucleus) and the transverse (sigma-arrow-right x qtau/sub lambda/) spin channels for a large range of momentum transfer (qapprox.0--600 MeV/c). We examine a number of effective rho-coupling schemes used in the literature. Using the finite-nucleus formalism of Toki and Weise, we examine in detail the response function in the presence of the rho-meson exchange term. The renormalization of matrix elements of spin-isospin sensitive probes is given for the J/sup P/ = 1 + , T = 1 level of 12 C. We analyze the results, gaining some insight into the nature of the longitudinal versus transverse channels and into approximations suggested in the past for handling finite-nucleus calculations. A comparison with local density approximation and infinite nuclear matter with a constant density results is presented for a variety of cases

Fierz transformations and renormalization schemes for fourquark operators

Directory of Open Access Journals (Sweden)

Garron Nicolas

2018-01-01

Full Text Available It has been shown that the choice of renormalization scheme is crucial for four-quark operators, in particular for neutral kaon mixing beyond the Standard Model. In the context of SMOM schemes, the choice of projector is not unique and is part of the definition of the renormalisation scheme. I present the non-diagonal Fierz relations which relate some of these projectors.

Nonthermal fixed points and the functional renormalization group

International Nuclear Information System (INIS)

Berges, Juergen; Hoffmeister, Gabriele

2009-01-01

Nonthermal fixed points represent basic properties of quantum field theories, in addition to vacuum or thermal equilibrium fixed points. The functional renormalization group on a closed real-time path provides a common framework for their description. For the example of an O(N) symmetric scalar theory it reveals a hierarchy of fixed point solutions, with increasing complexity from vacuum and thermal equilibrium to nonequilibrium

Study of the O(N) linear σ model at finite temperature using the 2PPI expansion

International Nuclear Information System (INIS)

Verschelde, H.; De Pessemier, J.

2002-01-01

We show that a new expansion, which sums seagull and bubble graphs to all orders, can be applied to the O(N) linear σ-model at finite temperature. We prove that this expansion can be renormalized with the usual counterterms in a mass independent scheme and that Goldstone's theorem is satisfied at each order. At the one loop order of this expansion, the Hartree result for the effective potential (daisy and superdaisy graphs) is recovered. We show that at one loop 2PPI order, the self-energy of the σ-meson can be calculated exactly and that diagrams are summed beyond the Hartree approximation. (orig.)

Application of the renormalization group to the study of structure function in the deep inelastic scattering

International Nuclear Information System (INIS)

Dias, S.A.

1985-01-01

The transformation law of truncated pertubation theory observables under changes of renormalization scheme is deduced. Based on this, a criticism of the calculus of the moments of structure functions in deep inelastic scattering, obtaining that the A 2 coefficient not renormalization group invariant is done. The PMS criterion is used to optimize the perturbative productions of the moments, truncated to 2nd order. (author) [pt

Renormalization of gauge theories in the background-field approach arXiv

CERN Document Server

Barvinsky, Andrei O.; Herrero-Valea, Mario; Sibiryakov, Sergey M.; Steinwachs, Christian F.

Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.

Four loop wave function renormalization in the non-abelian Thirring model

International Nuclear Information System (INIS)

Ali, D.B.; Gracey, J.A.

2001-01-01

We compute the anomalous dimension of the fermion field with N f flavours in the fundamental representation of a general Lie colour group in the non-abelian Thirring model at four loops. The implications on the renormalization of the two point Green's function through the loss of multiplicative renormalizability of the model in dimensional regularization due to the appearance of evanescent four fermi operators are considered at length. We observe the appearance of one new colour group Casimir, d F abcd d F abcd , in the final four loop result and discuss its consequences for the relation of the Knizhnik-Zamolodchikov critical exponents in the Wess-Zumino-Witten-Novikov model to the non-abelian Thirring model. Renormalization scheme changes are also considered to ensure that the underlying Fierz symmetry broken by dimensional regularization is restored

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.)

Renormalized plasma turbulence theory: A quasiparticle picture

International Nuclear Information System (INIS)

DuBois, D.F.

1981-01-01

A general renormalized statistical theory of Vlasov turbulence is given which proceeds directly from the Vlasov equation and does not assume prior knowledge of sophisticated field-theoretic techniques. Quasiparticles are the linear excitations of the turbulent system away from its instantaneous mean (ensemble-averaged) state or background; the properties of this background state ''dress'' or renormalize the quasiparticle responses. It is shown that all two-point responses (including the dielectric) and all two-point correlation functions can be completely described by the mean distribution function and three fundamental quantities. Two of these are the quasiparticle responses: the propagator and the potential source: which measure, respectively, the separate responses of the mean distribution function and the mean electrostatic potential to functional changes in an external phase-space source added to Vlasov's equation. The third quantity is the two-point correlation function of the incoherent part of the phase-space density which acts as a self-consistent source of quasiparticle and potential fluctuations. This theory explicitly takes into account the self-consistent nature of the electrostatic-field fluctuations which introduces new effects not found in the usual ''test-particle'' theories. Explicit equations for the fundamental quantities are derived in the direct interaction approximation. Special attention is paid to the two-point correlations and the relation to theories of phase-space granulation

Finite-width effects in unstable-particle production at hadron colliders

Energy Technology Data Exchange (ETDEWEB)

Falgari, P. [Utrecht Univ. (Netherlands). Inst. for Theoretical Physics; Utrecht Univ. (Netherlands). Spinoza Inst.; Papanastasiou, A.S. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Signer, A. [Paul Scherrer Institut, Villigen (Switzerland); Zuerich Univ. (Switzerland). Inst. for Theoretical Physics

2013-03-15

We present a general formalism for the calculation of finite-width contributions to the differential production cross sections of unstable particles at hadron colliders. In this formalism, which employs an effective-theory description of unstable-particle production and decay, the matrix element computation is organized as a gauge-invariant expansion in powers of {Gamma}{sub X}/m{sub X}, with {Gamma}{sub X} and m{sub X} the width and mass of the unstable particle. This framework allows for a systematic inclusion of off-shell and non-factorizable effects whilst at the same time keeping the computational effort minimal compared to a full calculation in the complex-mass scheme. As a proof-of-concept example, we give results for an NLO calculation of top-antitop production in the q anti q partonic channel. As already found in a similar calculation of single-top production, the finite-width effects are small for the total cross section, as expected from the naive counting {proportional_to}{Gamma}{sub t}/m{sub t}{proportional_to}1%. However, they can be sizeable, in excess of 10%, close to edges of certain kinematical distributions. The dependence of the results on the mass renormalization scheme, and its implication for a precise extraction of the top-quark mass, is also discussed.

Finite-width effects in unstable-particle production at hadron colliders

International Nuclear Information System (INIS)

Falgari, P.; Signer, A.; Zuerich Univ.

2013-03-01

We present a general formalism for the calculation of finite-width contributions to the differential production cross sections of unstable particles at hadron colliders. In this formalism, which employs an effective-theory description of unstable-particle production and decay, the matrix element computation is organized as a gauge-invariant expansion in powers of Γ X /m X , with Γ X and m X the width and mass of the unstable particle. This framework allows for a systematic inclusion of off-shell and non-factorizable effects whilst at the same time keeping the computational effort minimal compared to a full calculation in the complex-mass scheme. As a proof-of-concept example, we give results for an NLO calculation of top-antitop production in the q anti q partonic channel. As already found in a similar calculation of single-top production, the finite-width effects are small for the total cross section, as expected from the naive counting ∝Γ t /m t ∝1%. However, they can be sizeable, in excess of 10%, close to edges of certain kinematical distributions. The dependence of the results on the mass renormalization scheme, and its implication for a precise extraction of the top-quark mass, is also discussed.

Pairing renormalization and regularization within the local density approximation

International Nuclear Information System (INIS)

Borycki, P.J.; Dobaczewski, J.; Nazarewicz, W.; Stoitsov, M.V.

2006-01-01

We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure make it a method of choice for future applications

Renormalization group invariance in the presence of an instanton

International Nuclear Information System (INIS)

Ross, D.A.

1987-01-01

A pure Yang-Mills theory which admits an instanton is under discussion. n=1 supersymmetric (SU-2) Yang-Mills theory, both in the Wess-zumino gauge and in manifestly supersymmetric supergauge is considered. Two-loop vacuum graphs are calculated. The way a renormalization group invariance works under conditions of fermionic zero mode elimination is shown

Real-space renormalization group approach to driven diffusive systems

Energy Technology Data Exchange (ETDEWEB)

Hanney, T [SUPA and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ (United Kingdom); Stinchcombe, R B [Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP (United Kingdom)

2006-11-24

We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase.

Real-space renormalization group approach to driven diffusive systems

International Nuclear Information System (INIS)

Hanney, T; Stinchcombe, R B

2006-01-01

We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase

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.

A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

KAUST Repository

Wheeler, Mary; Xue, Guangri; Yotov, Ivan

2011-01-01

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields

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

Construction of renormalized coefficient functions of the Feynman diagrams by means of a computer

International Nuclear Information System (INIS)

Tarasov, O.V.

1978-01-01

An algorithm and short description of computer program, written in SCHOONSCHIP, are given. The program is assigned for construction of integrands of renormalized coefficient functions of the Feynman diagrams in scalar theories in the case of arbitrary subtraction point. For the given Feynman graph computer completely realizes the R-operation of Bogolubov-Parasjuk and gives the result as an integral over Feynman parameters. With the help of the program the time construction of the whole renormalized coefficient function is equal approximately 30 s on the CDC-6500 computer

Chaotic renormalization group approach to disordered systems

International Nuclear Information System (INIS)

Oliveira, P.M.C. de; Continentino, M.A.; Makler, S.S.; Anda, E.V.

1984-01-01

We study the eletronic properties of the disordered linear chain using a technique previously developed by some of the authors for an ordered chain. The equations of motion for the one electron Green function are obtained and the configuration average is done according to the GK scheme. The dynamical problem is transformed, using a renormalization group procedure, into a bidimensional map. The properties of this map are investigated and related to the localization properties of the eletronic system. (Author) [pt

Blockspin transformations for finite temperature field theories with gauge fields

International Nuclear Information System (INIS)

Kerres, U.

1996-08-01

A procedure is proposed to study quantum field theories at zero or at finite temperature by a sequence of real space renormalization group (RG) or blockspin transformations. They transform to effective theories on coarser and coarser lattices. The ultimate aim is to compute constraint effective potentials, i.e. the free energy as a function of suitable order parameters. From the free energy one can read off the thermodynamic behaviour of the theory, in particular the existence and nature of phase transitions. In a finite temperature field theory one begins with either one or a sequence of transformations which transform the original theory into an effective theory on a three-dimensional lattice. Its effective action has temperature dependent coefficients. Thereafter one may proceed with further blockspin transformations of the three-dimensional theory. Assuming a finite volume, this can in principle be continued until one ends with a lattice with a single site. Its effective action is the constraint effective potential. In each RG-step, an integral over the high frequency part of the field, also called the fluctuation field, has to be performed. This is done by perturbation theory. It requires the knowledge of bare fluctuation field propagators and of interpolation operators which enter into the vertices. A detailed examination of these quantities is presented for scalar fields, abelian gauge fields and for Higgs fields, finite temperature is admitted. The lattice perturbation theory is complicated because the bare lattice propagators are complicated. This is due to a partial loss of translation invariance in each step. Therefore the use of translation invariant cutoffs in place of a lattice is also discussed. In case of gauge fields this is only possible as a continuum version of the blockspin method. (orig.)

Renormalization of quark propagator, vertex functions, and twist-2 operators from twisted-mass lattice QCD at Nf=4

Science.gov (United States)

Blossier, Benoît.; Brinet, Mariane; Guichon, Pierre; Morénas, Vincent; Pène, Olivier; Rodríguez-Quintero, Jose; Zafeiropoulos, Savvas

2015-06-01

We present a precise nonperturbative determination of the renormalization constants in the mass independent RI'-MOM scheme. The lattice implementation uses the Iwasaki gauge action and four degenerate dynamical twisted-mass fermions. The gauge configurations are provided by the ETM Collaboration. Renormalization constants for scalar, pseudoscalar, vector and axial operators, as well as the quark propagator renormalization, are computed at three different values of the lattice spacing, two volumes and several twisted-mass parameters. The method we developed allows for a precise cross-check of the running, thanks to the particular proper treatment of hypercubic artifacts. Results for the twist-2 operator O44 are also presented.

Renormalization group coupling flow of SU(3) gauge theory

OpenAIRE

QCDTARO Collaboration

1998-01-01

We present our new results on the renormalization group coupling flow obtained i n 3 dimensional coupling space $(\\beta_{11},\\beta_{12},\\beta_{twist})$. The value of $\\beta_{twist}$ turns out to be small and the coupling flow projected on $(\\beta_{11},\\beta_{12})$ plane is very similar with the previous result obtained in the 2 dimensional coupling space.

Migdal-Kadanoff renormalization group for the Z(5) model

International Nuclear Information System (INIS)

Baltar, V.L.V.; Carneiro, G.M.; Pol, M.E.; Zagury, N.

1984-01-01

The Migdal-Kadanoff renormalization group methods is used to calculate the phase diagram of the AF Z(5) model. It is found that this scheme simulates a fixed line which it is interpreted as the locus of attraction of a critical phase. This result is in reasonable agreement with the predictions of Monte Carlo simulations. (Author) [pt

Superconformal gravity in Hamiltonian form: another approach to the renormalization of gravitation

International Nuclear Information System (INIS)

Kaku, M.

1983-01-01

We reexpress superconformal gravity in Hamiltonian form, explicitly displaying all 24 generators of the group as Dirac constraints on the Hilbert space. From this, we can establish a firm foundation for the canonical quantization of superconformal gravity. The purpose of writing down the Hamiltonian form of the theory is to reexamine the question of renormalization and unitarity. Usually, we start with unitary theories of gravity, such as the Einstein-Hilbert action or supergravity, both of which are probably not renormalizable. In this series of papers, we take the opposite approach and start with a theory which is renormalizable but has problems with unitarity. Conformal and superconformal gravity are both plagued with dipole ghosts when we use perturbation theory to quantize the theories. It is difficult to interpret the results of perturbation theory because the asymptotic states have zero norm and the potential between particles grows linearly with the separation distance. The purpose of writing the Hamiltonian form of these theories is to approach the question of unitarity from a different point of view. For example, a strong-coupling approach to these theories may yield a totally different perturbation expansion. We speculate that canonically quantizing the theory by power expanding in the strong-coupling regime may yield a different set of asymptotic states, somewhat similar to the situation in gauge theories. In this series of papers, we wish to reopen the question of the unitarity of conformal theories. We conjecture that ghosts are ''confined.''

Practical algebraic renormalization

International Nuclear Information System (INIS)

Grassi, Pietro Antonio; Hurth, Tobias; Steinhauser, Matthias

2001-01-01

A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the standard model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process B→X s γ

Fierz-complete NJL model study: Fixed points and phase structure at finite temperature and density

Science.gov (United States)

Braun, Jens; Leonhardt, Marc; Pospiech, Martin

2017-10-01

Nambu-Jona-Lasinio-type models are frequently employed as low-energy models in various research fields. With respect to the theory of the strong interaction, this class of models is indeed often used to analyze the structure of the phase diagram at finite temperature and quark chemical potential. The predictions from such models for the phase structure at finite quark chemical potential are of particular interest as this regime is difficult to access with lattice Monte Carlo approaches. In this work, we consider a Fierz-complete version of a Nambu-Jona-Lasinio model. By studying its renormalization group flow, we analyze in detail how Fierz-incomplete approximations affect the predictive power of such model studies. In particular, we investigate the curvature of the phase boundary at small chemical potential, the critical value of the chemical potential above which no spontaneous symmetry breaking occurs, and the possible interpretation of the underlying dynamics in terms of difermion-type degrees of freedom. We find that the inclusion of four-fermion channels other than the conventional scalar-pseudoscalar channel is not only important at large chemical potential but also leaves a significant imprint on the dynamics at small chemical potential as measured by the curvature of the finite-temperature phase boundary.

Experimental test of renormalization group theory on the uniaxial, dipolar coupled ferromagnet LiTbf4

DEFF Research Database (Denmark)

Als-Nielsen, Jens Aage

1976-01-01

The transverse correlation range ξ and the susceptibility in the critical region has been measured by neutron scattering. A special technique required to resolve the superdiverging longitudinal correlation range has been utilized. The results for ξ together with existing specific-heat data are in...... are in remarkable agreement with the renormalization group theory of systems with marginal dimensionality. The ratio between the susceptibility amplitudes above and below Tc was found to be 2 in accordance with renormalization-group and meanfield theory....

How to resolve the factorization- and the renormalization-scheme ambiguities simultaneously

International Nuclear Information System (INIS)

Nakkagawa, H.; Niegawa, A.

1982-01-01

A combined investigation of both the factorization- and renormalization-scheme dependences of perturbative QCD calculations is reported. Applyong Stevenson's optimization method, we get a remarkable result, which forces us to exponentiate 'everything' with uncorrected subprocess cross sections. (orig.)

Unraveling the interlayer-related phonon self-energy renormalization in bilayer graphene.

Science.gov (United States)

Araujo, Paulo T; Mafra, Daniela L; Sato, Kentaro; Saito, Riichiro; Kong, Jing; Dresselhaus, Mildred S

2012-01-01

In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS₂, WSe₂, oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications.

Renormalization of period doubling in symmetric four-dimensional volume-preserving maps

International Nuclear Information System (INIS)

Mao, J.; Greene, J.M.

1987-01-01

We have determined three maps (truncated at quadratic terms) that are fixed under the renormalization operator of pitchfork period doubling in symmetric four-dimensional volume-preserving maps. Each of these contains the previously known two-dimensional area-preserving map that is fixed under the period-doubling operator. One of these three fixed maps consists of two uncoupled two-dimensional (nonlinear) area-preserving fixed maps. The other two contain also the two-dimensional area-preserving fixed map coupled (in general) with a linear two-dimensional map. The renormalization calculation recovers all numerical results for the pitchfork period doubling in the symmetric four-dimensional volume-preserving maps, reported by Mao and Helleman [Phys. Rev. A 35, 1847 (1987)]. For a large class of nonsymmetric four-dimensional volume-preserving maps, we found that the fixed maps are the same as those for the symmetric maps

On the perturbative renormalization of four-quark operators for new physics

Energy Technology Data Exchange (ETDEWEB)

Papinutto, M. [Roma Univ. (Italy). Dipt. di Fisica; INFN, Sezione di Roma (Italy); Pena, C. [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC; Preti, D. [Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC

2017-06-15

We discuss the renormalization properties of the full set of ΔF = 2 operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schroedinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all ΔF = 1,2 operators in these schemes. Finally, we discuss the systematic uncertainties related to the use of NLO perturbation theory for the RG running of four-quark operators to scales in the GeV range, in both our SF schemes and standard MS and RI-MOM schemes. Large truncation effects are found for some of the operators considered. (orig.)

Renormalization group summation of Laplace QCD sum rules for scalar gluon currents

Directory of Open Access Journals (Sweden)

Farrukh Chishtie

2016-03-01

Full Text Available We employ renormalization group (RG summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter μ2 once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.

A density matrix renormalization group study of low-lying excitations ...

Indian Academy of Sciences (India)

Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited 2 symmetry and spin parity of the system to obtain excited states of ...

Introduction to the renormalization group study in relativistic quantum field theory

International Nuclear Information System (INIS)

Mignaco, J.A.; Roditi, I.

1985-01-01

An introduction to the renormalization group approach in relativistic quantum field theories is presented, beginning with a little historical about the subject. Further, this problem is discussed from the point of view of the perturbation theory. (L.C.) [pt

Renormalization group flow of entanglement entropy on spheres

Energy Technology Data Exchange (ETDEWEB)

Ben-Ami, Omer; Carmi, Dean [Raymond and Beverly Sackler Faculty of Exact Sciences School of Physics and Astronomy,Tel-Aviv University, Ramat-Aviv 69978 (Israel); Smolkin, Michael [Center for Theoretical Physics and Department of Physics,University of California, Berkeley, CA 94720 (United States)

2015-08-12

We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the bare couplings and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in d=2,3,4. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal ‘area law’ for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.

Gauge invariance and holographic renormalization

Directory of Open Access Journals (Sweden)

Keun-Young Kim

2015-10-01

Full Text Available We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalization: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry (RGS. By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.

Class renormalization: islands around islands

International Nuclear Information System (INIS)

Meiss, J.D.

1986-01-01

An orbit of 'class' is one that rotates about a periodic orbit of one lower class with definite frequency. This contrasts to the 'level' of a periodic orbit which is the number of elements in its continued fraction expansion. Level renormalization is conventionally used to study the structure of quasi-periodic orbits. The scaling structure of periodic orbits encircling other periodic orbits in area preserving maps is discussed here. Fixed points corresponding to the accumulation of p/q bifurcations are found and scaling exponents determined. Fixed points for q > 2 correspond to self-similar islands around islands. Frequencies of the island boundary circles at the fixed points are obtained. Importance of this scaling for the motion of particles in stochastic regions is emphasized. (author)

Finite-temperature dynamics of the Mott insulating Hubbard chain

Science.gov (United States)

Nocera, Alberto; Essler, Fabian H. L.; Feiguin, Adrian E.

2018-01-01

We study the dynamical response of the half-filled one-dimensional Hubbard model for a range of interaction strengths U and temperatures T by a combination of numerical and analytical techniques. Using time-dependent density matrix renormalization group computations we find that the single-particle spectral function undergoes a crossover to a spin-incoherent Luttinger liquid regime at temperatures T ˜J =4 t2/U for sufficiently large U >4 t . At smaller values of U and elevated temperatures the spectral function is found to exhibit two thermally broadened bands of excitations, reminiscent of what is found in the Hubbard-I approximation. The dynamical density-density response function is shown to exhibit a finite-temperature resonance at low frequencies inside the Mott gap, with a physical origin similar to the Villain mode in gapped quantum spin chains. We complement our numerical computations by developing an analytic strong-coupling approach to the low-temperature dynamics in the spin-incoherent regime.

Photon propagators and the definition and approximation of renormalized stress tensors in curved space-time

International Nuclear Information System (INIS)

Brown, M.R.; Ottewill, A.C.

1986-01-01

We present the symmetric Hadamard representation for scalar and photon Feynman Green's functions. We use these representations to give a simple definition for their associated renormalized stress tensors. We investigate the connection between the accuracy of the WKB approximation and the vanishing of the trace anomaly for these fields. We show that, although for scalars there is a direct connection, this is not true for photons, and we discuss the relevance of these results to the approximation of renormalized stress tensors in static Einstein space-times