On the renormalization of the effective field theory of large scale structures

Energy Technology Data Exchange (ETDEWEB)

Pajer, Enrico [Department of Physics, Princeton University, Princeton, NJ 08544 (United States); Zaldarriaga, Matias, E-mail: enrico.pajer@gmail.com, E-mail: matiasz@ias.edu [Institute for Advanced Study, Princeton, NJ 08544 (United States)

2013-08-01

Standard perturbation theory (SPT) for large-scale matter inhomogeneities is unsatisfactory for at least three reasons: there is no clear expansion parameter since the density contrast is not small on all scales; it does not fully account for deviations at large scales from a perfect pressureless fluid induced by short-scale non-linearities; for generic initial conditions, loop corrections are UV-divergent, making predictions cutoff dependent and hence unphysical. The Effective Field Theory of Large Scale Structures successfully addresses all three issues. Here we focus on the third one and show explicitly that the terms induced by integrating out short scales, neglected in SPT, have exactly the right scale dependence to cancel all UV-divergences at one loop, and this should hold at all loops. A particularly clear example is an Einstein deSitter universe with no-scale initial conditions P{sub in} ∼ k{sup n}. After renormalizing the theory, we use self-similarity to derive a very simple result for the final power spectrum for any n, excluding two-loop corrections and higher. We show how the relative importance of different corrections depends on n. For n ∼ −1.5, relevant for our universe, pressure and dissipative corrections are more important than the two-loop corrections.

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 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 ...

Excited state TBA and renormalized TCSA in the scaling Potts model

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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 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

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)

A renormalization group scaling analysis for compressible two-phase flow

International Nuclear Information System (INIS)

Chen, Y.; Deng, Y.; Glimm, J.; Li, G.; Zhang, Q.; Sharp, D.H.

1993-01-01

Computational solutions to the Rayleigh--Taylor fluid mixing problem, as modeled by the two-fluid two-dimensional Euler equations, are presented. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a renormalization group analysis. The computations, carried out with the front tracking method on an Intel iPSC/860, are highly resolved and statistical convergence of ensemble averages is achieved. The computations are consistent with the experimentally observed growth rates for nearly incompressible flows. The dynamics of the interior portion of the mixing zone is simplified by the use of scaling variables. The size of the mixing zone suggests fixed-point behavior. The profile of statistical quantities within the mixing zone exhibit self-similarity under fixed-point scaling to a limited degree. The effect of compressibility is also examined. It is found that, for even moderate compressibility, the growth rates fail to satisfy universal scaling, and moreover, increase significantly with increasing compressibility. The growth rates predicted from a renormalization group fixed-point model are in a reasonable agreement with the results of the exact numerical simulations, even for flows outside of the incompressible limit

Scheme-Independent Predictions in QCD: Commensurate Scale Relations and Physical Renormalization Schemes

International Nuclear Information System (INIS)

Brodsky, Stanley J.

1998-01-01

Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the ''generalized Crewther relation'', which connects the Bjorken and Gross-Llewellyn Smith deep inelastic scattering sum rules to measurements of the e + e - annihilation cross section. All non-conformal effects are absorbed by fixing the ratio of the respective momentum transfer and energy scales. In the case of fixed-point theories, commensurate scale relations relate both the ratio of couplings and the ratio of scales as the fixed point is approached. The relations between the observables are independent of the choice of intermediate renormalization scheme or other theoretical conventions. Commensurate scale relations also provide an extension of the standard minimal subtraction scheme, which is analytic in the quark masses, has non-ambiguous scale-setting properties, and inherits the physical properties of the effective charge α V (Q 2 ) defined from the heavy quark potential. The application of the analytic scheme to the calculation of quark-mass-dependent QCD corrections to the Z width is also reviewed

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.

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.

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.

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

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.

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.)

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 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

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 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

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

Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

Energy Technology Data Exchange (ETDEWEB)

Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

2006-12-15

In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

International Nuclear Information System (INIS)

Actis, S.; Passarino, G.

2006-12-01

In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

Simultaneous analysis in renormalization and factorization scheme dependences in perturbative QCD

International Nuclear Information System (INIS)

Nakkagawa, Hisao; Niegawa, Akira.

1983-01-01

Combined and thorough investigations of both the factorization and the renormalization scheme dependences of perturbative QCD calculations are given. Our findings are that (i) by introducing a multiscale-dependent coupling the simultaneous parametrization of both scheme-dependences can be accomplished, (ii) Stevenson's optimization method works quite well so that it gives a remarkable prediction which forces us to exponentiate ''everything'' with uncorrected subprocess cross sections, and (iii) the perturbation series in QCD may converge when Stevenson's principle of minimal sensitivity is taken into account at each order of perturbative approximation. (author)

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

Renormalization, Wilson lines, and transverse-momentum-dependent parton-distribution functions

International Nuclear Information System (INIS)

Cherednikov, I. O.; Stefanis, N. G.

2008-01-01

We perform an analysis of transverse-momentum dependent parton-distribution functions, making use of their renormalization properties in terms of their leading-order anomalous dimensions. We show that the appropriate Wilson line in the light cone gauge, associated with such quantities, is a cusped one at light cone infinity. To cancel the ensuing cusp anomalous dimension, we include in the definition of the transverse-momentum dependent parton-distribution functions an additional soft counter term (gauge link) along that cusped transverse contour. We demonstrate that this is tantamount to an 'intrinsic (Coulomb) phase', which accumulates the full gauge history of the color-charged particle.

Material and Doping Dependence of the Nodal and Anti-Nodal Dispersion Renormalizations in Single- and Multi-Layer Cuprates

Energy Technology Data Exchange (ETDEWEB)

Johnston, S.; /Waterloo U. /SLAC; Lee, W.S.; /Stanford U., Geballe Lab. /SLAC; Nowadnick, E.A.; /SLAC /Stanford U., Phys. Dept.; Moritz, B.; /SLAC /North Dakota U.; Shen, Z.-X.; /Stanford U., Geballe Lab. /SLAC /Stanford U., Phys. Dept. /Stanford U., Appl. Phys. Dept.; Devereaux, T.P.; /Stanford U., Geballe Lab. /SLAC

2010-02-15

In this paper we present a review of bosonic renormalization effects on electronic carriers observed from angle-resolved photoemission spectra in the cuprates. Specifically, we discuss the viewpoint that these renormalizations represent coupling of the electrons to the lattice and review how materials dependence, such as the number of CuO{sub 2} layers, and doping dependence can be understood straightforwardly in terms of several aspects of electron-phonon coupling in layered correlated materials.

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)

Studies in the renormalization-prescription dependence of perturbative calculations

International Nuclear Information System (INIS)

Celmaster, W.; Sivers, D.

1981-01-01

Now that the quantitative testing of perturbative quantum chromodynamics (QCD) has become a major experimental and theoretical effort, it is important to understand the renormalization-prescription dependence of perturbative calculations. We stress the phenomenological importance of finding a definition of the QCD expansion parameter which reduces the magnitude of high-order corrections. We give explicit arguments suggesting that a choice of coupling based on momentum-space subtraction can be phenomenologically useful. Examples from QCD and QED are used to illustrate these arguments, and we also discuss possibilities for refining them

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

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.)

Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system.

Science.gov (United States)

Goh, Segun; Lee, Keumsook; Choi, Moo Young; Fortin, Jean-Yves

2014-01-01

Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system.

Directory of Open Access Journals (Sweden)

Segun Goh

Full Text Available Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare bus stops are transformed into a (renormalized "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

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.

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.)

Threshold effects on renormalization group running of neutrino parameters in the low-scale seesaw model

International Nuclear Information System (INIS)

Bergstroem, Johannes; Ohlsson, Tommy; Zhang He

2011-01-01

We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC).

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.

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

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.

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.

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.)

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.

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.

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)

Self-energy renormalization for inhomogeneous nonequilibrium systems and field expansion via complete set of time-dependent wavefunctions

Science.gov (United States)

Kuwahara, Y.; Nakamura, Y.; Yamanaka, Y.

2018-04-01

The way to determine the renormalized energy of inhomogeneous systems of a quantum field under an external potential is established for both equilibrium and nonequilibrium scenarios based on thermo field dynamics. The key step is to find an extension of the on-shell concept valid in homogeneous case. In the nonequilibrium case, we expand the field operator by time-dependent wavefunctions that are solutions of the appropriately chosen differential equation, synchronizing with temporal change of thermal situation, and the quantum transport equation is derived from the renormalization procedure. Through numerical calculations of a triple-well model with a reservoir, we show that the number distribution and the time-dependent wavefunctions are relaxed consistently to the correct equilibrium forms at the long-term limit.

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

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.

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)

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)

Renormalization of fermion mixing

International Nuclear Information System (INIS)

Schiopu, R.

2007-01-01

hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories. (orig.)

Renormalization of fermion mixing

Energy Technology Data Exchange (ETDEWEB)

Schiopu, R.

2007-05-11

hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories. (orig.)

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 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.)

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.

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.)

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...

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.)

Temperature-Dependent Mollow Triplet Spectra from a Single Quantum Dot: Rabi Frequency Renormalization and Sideband Linewidth Insensitivity

DEFF Research Database (Denmark)

Wei, Yu-Jia; He, Yu; He, Yu-Ming

2014-01-01

We investigate temperature-dependent resonance fluorescence spectra obtained from a single self- assembled quantum dot. A decrease of the Mollow triplet sideband splitting is observed with increasing temperature, an effect we attribute to a phonon-induced renormalization of the driven dot Rabi fr...

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.

Perturbative determination of mass-dependent renormalization and improvement coefficients for the heavy-light vector and axial-vector currents with relativistic heavy and domain-wall light quarks

International Nuclear Information System (INIS)

Yamada, Norikazu; Aoki, Sinya; Kuramashi, Yoshinobu

2005-01-01

We determine the mass-dependent renormalization as well as improvement coefficients for the heavy-light vector and axial-vector currents consisting of the relativistic heavy and the domain-wall light quarks through the standard matching procedure. The calculation is carried out perturbatively at the one-loop level to remove the systematic error of O(α s (am Q ) n ap) as well as O(α s (am Q ) n ) (n>=0), where p is a typical momentum scale in the heavy-light system. We point out that renormalization and improvement coefficients of the heavy-light vector current agree with those of the axial-vector current, thanks to the exact chiral symmetry for the light quark. The results obtained with three different gauge actions, plaquette, Iwasaki and DBW2, are presented as a function of heavy quark mass and domain-wall height

Effects of renormalizing the chiral SU(2) quark-meson model

Science.gov (United States)

Zacchi, Andreas; Schaffner-Bielich, Jürgen

2018-04-01

We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.

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).

On the Soft Limit of the Large Scale Structure Power Spectrum: UV Dependence

CERN Document Server

Garny, Mathias; Porto, Rafael A; Sagunski, Laura

2015-01-01

We derive a non-perturbative equation for the large scale structure power spectrum of long-wavelength modes. Thereby, we use an operator product expansion together with relations between the three-point function and power spectrum in the soft limit. The resulting equation encodes the coupling to ultraviolet (UV) modes in two time-dependent coefficients, which may be obtained from response functions to (anisotropic) parameters, such as spatial curvature, in a modified cosmology. We argue that both depend weakly on fluctuations deep in the UV. As a byproduct, this implies that the renormalized leading order coefficient(s) in the effective field theory (EFT) of large scale structures receive most of their contribution from modes close to the non-linear scale. Consequently, the UV dependence found in explicit computations within standard perturbation theory stems mostly from counter-term(s). We confront a simplified version of our non-perturbative equation against existent numerical simulations, and find good agr...

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

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.

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.)

Indefinite metric fields and the renormalization group

International Nuclear Information System (INIS)

Sherry, T.N.

1976-11-01

The renormalization group equations are derived for the Green functions of an indefinite metric field theory. In these equations one retains the mass dependence of the coefficient functions, since in the indefinite metric theories the masses cannot be neglected. The behavior of the effective coupling constant in the asymptotic and infrared limits is analyzed. The analysis is illustrated by means of a simple model incorporating indefinite metric fields. The model scales at first order, and at this order also the effective coupling constant has both ultra-violet and infra-red fixed points, the former being the bare coupling constant

A geometric renormalization group in discrete quantum space-time

International Nuclear Information System (INIS)

Requardt, Manfred

2003-01-01

We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalization group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that this process may generate a fixed limit phase, representing our continuous space-time on a mesoscopic or macroscopic scale, provided that the underlying discrete geometry is critical in a specific sense (geometric long range order). Our point of view is corroborated by a series of analytic and numerical results, which allow us to keep track of the geometric changes, taking place on the various scales of the resolution of space-time. Of particular conceptual importance are the notions of dimension of such random systems on the various scales and the notion of geometric criticality

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

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 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.

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

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.

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 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 Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology

CERN Document Server

Alonso, Rodrigo; Manohar, Aneesh V; Trott, Michael

2014-01-01

We calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the $\\lambda$ and Yukawa coupling terms completes the calculation of the one-loop anomalous dimension matrix for the dimension-six operators. There are 1350 $CP$-even and $1149$ $CP$-odd parameters in the dimension-six Lagrangian for 3 generations, and our results give the entire $2499 \\times 2499$ anomalous dimension matrix. We discuss how the renormalization of the dimension-six operators, and the additional renormalization of the dimension $d \\le 4$ terms of the SM Lagrangian due to dimension-six operators, lays the groundwork for future precision studies of the SM EFT aimed at constraining the effects of new physics through precision measurements at the electroweak scale. As some sample applications, we discuss some aspects of the full RGE improved result for essential processes such as $gg \\to h...

Renormalized action improvements

International Nuclear Information System (INIS)

Zachos, C.

1984-01-01

Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references

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.)

Turbulent mixing of a critical fluid: The non-perturbative renormalization

Directory of Open Access Journals (Sweden)

M. Hnatič

2018-01-01

Full Text Available Non-perturbative Renormalization Group (NPRG technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi〉∼(Pji⊥+αPji∥/kd+ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow, but there is a new nonequilibrium regime (universality class associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ of possible scaling regimes in the system. The physical point d=3, ζ=4/3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α≲2.26. Otherwise, in the case of “strong compressibility” α≳2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

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

Functional renormalization group approach to the Yang-Lee edge singularity

Energy Technology Data Exchange (ETDEWEB)

An, X. [Department of Physics, University of Illinois at Chicago,845 W. Taylor St., Chicago, IL 60607 (United States); Mesterházy, D. [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland); Stephanov, M.A. [Department of Physics, University of Illinois at Chicago,845 W. Taylor St., Chicago, IL 60607 (United States)

2016-07-08

We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3≤d≤6 Euclidean dimensions. We find very good agreement with high-temperature series data in d=3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ=6−d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂{sup 4}) truncations of the scale-dependent effective action.

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)

Commensurate scale relations: Precise tests of quantum chromodynamics without scale or scheme ambiguity

International Nuclear Information System (INIS)

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

1994-10-01

We derive commensurate scale relations which relate perturbatively calculable QCD observables to each other, including the annihilation ratio R e+ e - , the heavy quark potential, τ decay, and radiative corrections to structure function sum rules. For each such observable one can define an effective charge, such as α R (√s)/π ≡ R e+ e - (√s)/(3Σe q 2 )-1. The commensurate scale relation connecting the effective charges for observables A and B has the form α A (Q A ) α B (Q B )(1 + r A/Bπ / αB + hor-ellipsis), where the coefficient r A/B is independent of the number of flavors ∫ contributing to coupling renormalization, as in BLM scale-fixing. The ratio of scales Q A /Q B is unique at leading order and guarantees that the observables A and B pass through new quark thresholds at the same physical scale. In higher orders a different renormalization scale Q n* is assigned for each order n in the perturbative series such that the coefficients of the series are identical to that of a invariant theory. The commensurate scale relations and scales satisfy the renormalization group transitivity rule which ensures that predictions in PQCD are independent of the choice of an intermediate renormalization scheme C. In particular, scale-fixed predictions can be made without reference to theoretically constructed singular renormalization schemes such as MS. QCD can thus be tested in a new and precise way by checking that the effective charges of observables track both in their relative normalization and in their commensurate scale dependence. The commensurate scale relations which relate the radiative corrections to the annihilation ratio R e + e - to the radiative corrections for the Bjorken and Gross-Llewellyn Smith sum rules are particularly elegant and interesting

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)

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.

Anatomy of the magnetic catalysis by renormalization-group method

Science.gov (United States)

Hattori, Koichi; Itakura, Kazunori; Ozaki, Sho

2017-12-01

We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger-Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu-Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

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.)

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.

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

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.

Probing the desert by the two-loop renormalization-group equations

International Nuclear Information System (INIS)

Tanimoto, M.; Suetake, Y.; Senba, K.

1987-01-01

We have reexamined the study of probing the desert with fermion masses, presented by Bagger, Dimopoulos, and Masso, by using the two-loop renormalization-group equations in the framework of the SU(3) x SU(2) x U(1) model with three generations and one Higgs doublet. The blow-up energy scale of the Yukawa coupling is found to be dependent on the Higgs quartic coupling λ. If the Yukawa coupling blows up between the electroweak scale M/sub W/ and the grand unified scale M/sub X/, the Higgs potential is destabilized for small values of λ at the electroweak scale M/sub W/, and becomes strongly coupled for large values of λ at M/sub W/. It is found that the Higgs-scalar mass as well as the fermion masses are important to probe the desert

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.

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 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.)

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.

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

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.)

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

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

Anatomy of the magnetic catalysis by renormalization-group method

Directory of Open Access Journals (Sweden)

Koichi Hattori

2017-12-01

Full Text Available We first examine the scaling argument for a renormalization-group (RG analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger–Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu–Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Science.gov (United States)

Garkusha, A. V.; Kataev, A. L.; Molokoedov, V. S.

2018-02-01

The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU( N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the O({a}_s^4) level of perturbation theory. It is known that in the gauge-invariant renormalization \\overline{MS} -scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the \\overline{MS} -scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the O({a}_s^3) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = -3 , -1 and ξ = 0. In the O({a}_s^4) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = -3 at the O({a}_s^3) approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

On the soft limit of the large scale structure power spectrum. UV dependence

International Nuclear Information System (INIS)

Garny, Mathias

2015-08-01

We derive a non-perturbative equation for the large scale structure power spectrum of long-wavelength modes. Thereby, we use an operator product expansion together with relations between the three-point function and power spectrum in the soft limit. The resulting equation encodes the coupling to ultraviolet (UV) modes in two time-dependent coefficients, which may be obtained from response functions to (anisotropic) parameters, such as spatial curvature, in a modified cosmology. We argue that both depend weakly on fluctuations deep in the UV. As a byproduct, this implies that the renormalized leading order coefficient(s) in the effective field theory (EFT) of large scale structures receive most of their contribution from modes close to the non-linear scale. Consequently, the UV dependence found in explicit computations within standard perturbation theory stems mostly from counter-term(s). We confront a simplified version of our non-perturbative equation against existent numerical simulations, and find good agreement within the expected uncertainties. Our approach can in principle be used to precisely infer the relevance of the leading order EFT coefficient(s) using small volume simulations in an 'anisotropic separate universe' framework. Our results suggest that the importance of these coefficient(s) is a ∝ 10% effect, and plausibly smaller.

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.)

Exact CTP renormalization group equation for the coarse-grained effective action

International Nuclear Information System (INIS)

Dalvit, D.A.; Mazzitelli, F.D.

1996-01-01

We consider a scalar field theory in Minkowski spacetime and define a coarse-grained closed time path (CTP) effective action by integrating quantum fluctuations of wavelengths shorter than a critical value. We derive an exact CTP renormalization group equation for the dependence of the effective action on the coarse-graining scale. We solve this equation using a derivative expansion approach. Explicit calculation is performed for the λφ 4 theory. We discuss the relevance of the CTP average action in the study of nonequilibrium aspects of phase transitions in quantum field theory. copyright 1996 The American Physical Society

Two-loop renormalization in the standard model, part II. Renormalization procedures and computational techniques

Energy Technology Data Exchange (ETDEWEB)

Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

2006-12-15

In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, are discussed in part III where numerical results, e.g. for the complex poles of the unstable gauge bosons, are shown. An attempt is made to define the running of the electromagnetic coupling constant at the two-loop level. (orig.)

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

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

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.

Non-perturbative renormalization of quark bilinear operators with N{sub f}=2 (tmQCD) Wilson fermions and the tree-level improved gauge action

Energy Technology Data Exchange (ETDEWEB)

Constantinou, M. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Dimopoulos, P. [Roma ' ' La Sapienza' ' Univ. (Italy). Dipt. di Fisica; INFN, Rome (Italy); Frezzotti, R. [Roma ' ' Tor Vergata' ' Univ. (Italy). Dipt. di Fisica; INFN, Roma (IT)] (and others)

2010-06-15

We present results for the renormalization constants of bilinear quark operators obtained b4>UNL<426>UNL using the tree-level Symanzik improved gauge action and the N{sub f}=2 twisted mass fermion action at maximal twist, which guarantees automatic O(a)- improvement. Our results are also relevant for the corresponding standard (untwisted) Wilson fermionic action since the two actions only differ, in the massless limit, by a chiral rotation of the quark fields. The scale-independent renormalization constants Z{sub V}, Z{sub A} and the ratio Z{sub P}/Z{sub S} have been computed using the RI-MOM approach, as well as other alternative methods. For Z{sub A} and Z{sub P}/Z{sub S}, the latter are based on both standard twisted mass and Osterwalder-Seiler fermions, while for Z{sub V} a Ward Identity has been used. The quark field renormalization constant Z{sub q} and the scale dependent renormalization constants Z{sub S}, Z{sub P} and Z{sub T} are determined in the RI-MOM scheme. Leading discretization effects of O(g{sup 2}a{sup 2}), evaluated in one-loop perturbation theory, are explicitly subtracted from the RI-MOM estimates. (orig.)

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

Problems with the definition of renormalized Hamiltonians for momentum-space renormalization transformations

NARCIS (Netherlands)

Enter, Aernout C.D. van; Fernández, Roberto

For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the

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.)

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.

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

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)

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)

Renormalization group, operator product expansion and anomalous scaling in models of turbulent advection

International Nuclear Information System (INIS)

Antonov, N V

2006-01-01

Recent progress on the anomalous scaling in models of turbulent heat and mass transport is reviewed with the emphasis on the approach based on the field-theoretic renormalization group (RG) and operator product expansion (OPE). In that approach, the anomalous scaling is established as a consequence of the existence in the corresponding field-theoretic models of an infinite number of 'dangerous' composite fields (operators) with negative critical dimensions, which are identified with the anomalous exponents. This allows one to calculate the exponents in a systematic perturbation expansion, similar to the ε expansion in the theory of critical phenomena. The RG and OPE approach is presented in a self-contained way for the example of a passive scalar field (temperature, concentration of an impurity, etc) advected by a self-similar Gaussian velocity ensemble with vanishing correlation time, the so-called Kraichnan's rapid-change model, where the anomalous exponents are known up to order O(ε 3 ). Effects of anisotropy, compressibility and the correlation time of the velocity field are discussed. Passive advection by non-Gaussian velocity field governed by the stochastic Navier-Stokes equation and passively advected vector (e.g. magnetic) fields are considered

The metric on field space, functional renormalization, and metric–torsion quantum gravity

International Nuclear Information System (INIS)

Reuter, Martin; Schollmeyer, Gregor M.

2016-01-01

Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein–Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and “tetrad-only” gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.

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

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

Finite cluster renormalization and new two step renormalization group for Ising model

International Nuclear Information System (INIS)

Benyoussef, A.; El Kenz, A.

1989-09-01

New types of renormalization group theory using the generalized Callen identities are exploited in the study of the Ising model. Another type of two-step renormalization is proposed. Critical couplings and critical exponents y T and y H are calculated by these methods for square and simple cubic lattices, using different size clusters. (author). 17 refs, 2 tabs

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.)

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...

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

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)

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

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.

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal F (ϕ )R coupling

Science.gov (United States)

Merzlikin, Boris S.; Shapiro, Ilya L.; Wipf, Andreas; Zanusso, Omar

2017-12-01

Using covariant methods, we construct and explore the Wetterich equation for a nonminimal coupling F (ϕ )R of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered nonminimal coupling ξ ϕ2R as a special case. We consider the truncations without and with scale- and field-dependent wave-function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the nonminimal coupling in the symmetric and spontaneously broken phases with vanishing and nonvanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension d =4 .

Renormalized semiclassical quantization for rescalable Hamiltonians

International Nuclear Information System (INIS)

Takahashi, Satoshi; Takatsuka, Kazuo

2004-01-01

A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum

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

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-group analysis of the generalized sine-Gordon model and of the Coulomb gas for d≥3 dimensions

International Nuclear Information System (INIS)

Nandori, I.; Jentschura, U.D.; Soff, G.; Sailer, K.

2004-01-01

Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d≥3 of dimensions by means of the Wegner-Houghton method, and by way of the real-space RG approach. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d≥3, independent of the dimensionality, and in sharp contrast to the special case d=2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations) that the blocked potential tends to a constant effective potential in the infrared limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used

Renormalization Methods - A Guide For Beginners

International Nuclear Information System (INIS)

Cardy, J

2004-01-01

on rather oversimplified and unrelated models in the first part of the book that, in the end, the reader is left breathless on the threshold of the really interesting material. Despite the earlier emphasis on the application of renormalization ideas in dynamics, in the end the full power of the field-theoretical approach is not applied to the obvious arena of dynamic critical phenomena (where there certainly is currently a gap in the literature) but to the Navier--Stokes equations. The development of the book is somewhat illogical in places. Mean field theory interrupts discussion of block spin methods and scaling arguments---the two are distinct approaches. The Callan--Symanzik equation is introduced before Feynman diagrams are explained, so that there is a hiatus before the actual results for the critical exponents can be found. I think this book is too broad in some respects, and too limited in others, to be a really useful textbook for a course on renormalization methods. Those who have learned these ideas either from field theory, or from nonlinear systems, will find it more rewarding for the sections covering the topics with which they are less familiar. For this reason alone, the book should at least find a place on most library reference shelves. (book review)

Source Localization by Entropic Inference and Backward Renormalization Group Priors

Directory of Open Access Journals (Sweden)

Nestor Caticha

2015-04-01

Full Text Available A systematic method of transferring information from coarser to finer resolution based on renormalization group (RG transformations is introduced. It permits building informative priors in finer scales from posteriors in coarser scales since, under some conditions, RG transformations in the space of hyperparameters can be inverted. These priors are updated using renormalized data into posteriors by Maximum Entropy. The resulting inference method, backward RG (BRG priors, is tested by doing simulations of a functional magnetic resonance imaging (fMRI experiment. Its results are compared with a Bayesian approach working in the finest available resolution. Using BRG priors sources can be partially identified even when signal to noise ratio levels are up to ~ -25dB improving vastly on the single step Bayesian approach. For low levels of noise the BRG prior is not an improvement over the single scale Bayesian method. Analysis of the histograms of hyperparameters can show how to distinguish if the method is failing, due to very high levels of noise, or if the identification of the sources is, at least partially possible.

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.

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)

Renormalization scheme-dependence of perturbative quantum chromodynamics corrections to quarkonia

International Nuclear Information System (INIS)

Dentamaro, A.V.

1985-05-01

QCD radiative corrections to physical quantities are studied using Stevenson's principle of minimal sensitivity (PMS) to define the renormalization. We examine several naive potentials (Cornell group, power law and logarithmic), as well as the more sophisticated Richardson model in order to determine the spectra for the non-relativistic heavy charmonium and bottomonium systems. Predictions are made for the values of hyperfine splittings, leptonic and hadronic decay widths and E1 transition rates for these families of mesons. It is shown that good agreement with experimental data may be achieved by using a constant value of Λ/sub QCD/, which is determined by the PMS scheme and the potential model

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.

Renormalized sum rules for structure functions of heavy meson decays

International Nuclear Information System (INIS)

Grozin, A.G.; Korchemsky, G.P.

1996-01-01

We consider the properties of the structure functions of inclusive heavy meson decays B→X c and treat the c quark mass as a free parameter. We show that in two extreme cases of heavy and light c quarks the structure functions of heavy-heavy and heavy-light transitions are given by a Fourier transform of the matrix elements of Wilson lines containing a timelike and a lightlike segment, correspondingly. Using the renormalization properties of Wilson lines we find the dependence of the structure functions on the factorization scale, the structure function of the heavy-heavy transition is renormalized multiplicatively, while that of the heavy-light transition obeys the GLAP-type evolution equation. We propose a generalization of the sum rules for the moments of the structure functions (Bjorken, Voloshin, and the open-quote open-quote third close-quote close-quote sum rules) with a soft exponential factorization cutoff, which correctly incorporates both perturbative and nonperturbative effects. We analyze nonperturbative corrections by first considering infrared renormalon contributions to the Wilson lines. Uncertainties induced by the leading renormalon pole at u=1/2 are exactly canceled by a similar uncertainty in the heavy quark pole mass. The leading nonperturbative corrections associated with the next renormalon at u=1 are parametrized by the matrix element μ π 2 which is proportional to the heavy quark kinetic energy. copyright 1996 The American Physical Society

Entanglement renormalization, quantum error correction, and bulk causality

Energy Technology Data Exchange (ETDEWEB)

Kim, Isaac H. [IBM T.J. Watson Research Center,1101 Kitchawan Rd., Yorktown Heights, NY (United States); Kastoryano, Michael J. [NBIA, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen (Denmark)

2017-04-07

Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

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.

Renormalization and Central limit theorem for critical dynamical systems with weak external noise

CERN Document Server

Diaz-Espinosa, O

2006-01-01

We study of the effect of weak noise on critical one dimensional maps; that is, maps with a renormalization theory. We establish a one dimensional central limit theorem for weak noises and obtain Berry--Esseen estimates for the rate of this convergence. We analyze in detail maps at the accumulation of period doubling and critical circle maps with golden mean rotation number. Using renormalization group methods, we derive scaling relations for several features of the effective noise after long times. We use these scaling relations to show that the central limit theorem for weak noise holds in both examples. We note that, for the results presented here, it is essential that the maps have parabolic behavior. They are false for hyperbolic orbits.

Renormalization group procedure for potential −g/r2

Directory of Open Access Journals (Sweden)

S.M. Dawid

2018-02-01

Full Text Available Schrödinger equation with potential −g/r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r=0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

Holographic renormalization group and cosmology in theories with quasilocalized gravity

International Nuclear Information System (INIS)

Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John

2001-01-01

We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations

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

Benchmarking time-dependent renormalized natural orbital theory with exact solutions for a laser-driven model helium atom

Energy Technology Data Exchange (ETDEWEB)

Brics, Martins

2016-12-09

Intense, ultra-short laser pulses interacting with atoms, molecules, clusters, and solids give rise to many new fascinating phenomena, not at all accessible to quantum mechanics textbook perturbation theory. A full numerical solution of the time-dependent Schr¨odinger equation (TDSE) for such strong-field problems is also impossible for more than two electrons. Hence, powerful time-dependent quantum many-body approaches need to be developed. Unfortunately, efficient methods such as time-dependent density functional theory (TDDFT) fail in reproducing experimental observations, in particular if strong correlations are involved. In TDDFT, the approximation not only lies in the so-called exchange correlation potential but also in the density functionals for the observables of interest. In fact, with just the single-particle density alone it is unclear how to calculate, e.g., multiple-ionization probabilities or photoelectron spectra, or, even worse, correlated photoelectron spectra, as measured in nowadays experiments. In general, the simple structure of the time-dependent many-body Schroedinger equation for a highly-dimensional many-body wavefunction can only be traded for more complicated equations of motion for simpler quantities. In this thesis, a theory is examined that goes one step beyond TDDFT as far as the complexity of the propagated quantity is concerned. In time-dependent renormalized natural orbital theory (TDRNOT), the basic quantities that are propagated in time are the eigenvalues and eigenstates of the one-body reduced density matrix (1-RDM). The eigenstates are called natural orbitals (NOs), the eigenvalues are the corresponding occupation numbers (ONs). Compared to TDDFT, the knowledge of the NOs and the ONs relax the problem of calculating observables in practice because they can be used to construct the 1-RDM and the two-body reduced density matrix (2-RDM). After the derivation of the equations of motion for a combination of NOs and ONs, the so

Benchmarking time-dependent renormalized natural orbital theory with exact solutions for a laser-driven model helium atom

International Nuclear Information System (INIS)

Brics, Martins

2016-01-01

Intense, ultra-short laser pulses interacting with atoms, molecules, clusters, and solids give rise to many new fascinating phenomena, not at all accessible to quantum mechanics textbook perturbation theory. A full numerical solution of the time-dependent Schr¨odinger equation (TDSE) for such strong-field problems is also impossible for more than two electrons. Hence, powerful time-dependent quantum many-body approaches need to be developed. Unfortunately, efficient methods such as time-dependent density functional theory (TDDFT) fail in reproducing experimental observations, in particular if strong correlations are involved. In TDDFT, the approximation not only lies in the so-called exchange correlation potential but also in the density functionals for the observables of interest. In fact, with just the single-particle density alone it is unclear how to calculate, e.g., multiple-ionization probabilities or photoelectron spectra, or, even worse, correlated photoelectron spectra, as measured in nowadays experiments. In general, the simple structure of the time-dependent many-body Schroedinger equation for a highly-dimensional many-body wavefunction can only be traded for more complicated equations of motion for simpler quantities. In this thesis, a theory is examined that goes one step beyond TDDFT as far as the complexity of the propagated quantity is concerned. In time-dependent renormalized natural orbital theory (TDRNOT), the basic quantities that are propagated in time are the eigenvalues and eigenstates of the one-body reduced density matrix (1-RDM). The eigenstates are called natural orbitals (NOs), the eigenvalues are the corresponding occupation numbers (ONs). Compared to TDDFT, the knowledge of the NOs and the ONs relax the problem of calculating observables in practice because they can be used to construct the 1-RDM and the two-body reduced density matrix (2-RDM). After the derivation of the equations of motion for a combination of NOs and ONs, the so

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.

The renormalization of the electroweak standard model

International Nuclear Information System (INIS)

Boehm, M.; Spiesberger, H.; Hollik, W.

1984-03-01

A renormalization scheme for the electroweak standard model is presented in which the electric charge and the masses of the gauge bosons, Higgs particle and fermions are used as physical parameters. The photon is treated such that quantum electrodynamics is contained in the usual form. Field renormalization respecting the gauge symmetry gives finite Green functions. The Ward identities between the Green functions of the unphysical sector allow a renormalization that maintains the simple pole structure of the propagators. Explicit results for the renormalization self energies and vertex functions are given. They can be directly used as building blocks for the evaluation of l-loop radiative corrections. (orig.)

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.)

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.

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 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

Aspects of renormalization in finite-density field theory

Energy Technology Data Exchange (ETDEWEB)

Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia

2015-05-26

We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

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 renormalization for antiferromagnetism and superconductivity in the Hubbard model

International Nuclear Information System (INIS)

Friederich, Simon

2010-01-01

Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T c cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)

Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model

Energy Technology Data Exchange (ETDEWEB)

Friederich, Simon

2010-12-08

Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)

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)

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

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.)

Large neutrino mixing from renormalization group evolution

International Nuclear Information System (INIS)

Balaji, K.R.S.; Mohapatra, R.N.; Parida, M.K.; Paschos, E.A.

2000-10-01

The renormalization group evolution equation for two neutrino mixing is known to exhibit nontrivial fixed point structure corresponding to maximal mixing at the weak scale. The presence of the fixed point provides a natural explanation of the observed maximal mixing of ν μ - ν τ , if the ν μ and ν τ are assumed to be quasi-degenerate at the seesaw scale without constraining the mixing angles at that scale. In particular, it allows them to be similar to the quark mixings as in generic grand unified theories. We discuss implementation of this program in the case of MSSM and find that the predicted mixing remains stable and close to its maximal value, for all energies below the O(TeV) SUSY scale. We also discuss how a particular realization of this idea can be tested in neutrinoless double beta decay experiments. (author)

Application of dimensional regularization to single chain polymer static properties: Conformational space renormalization of polymers. III

International Nuclear Information System (INIS)

Oono, Y.; Ohta, T.; Freed, K.F.

1981-01-01

A dimensional regularization approach to the renormalization group treatment of polymer excluded volume is formulated in chain conformation space where monomers are specified by their spatial positions and their positions along the chain and the polymers may be taken to be monodisperse. The method utilizes basic scale invariance considerations. First, it is recognized that long wavelength macroscopic descriptions must be well defined in the limit that the minimum atomic or molecular scale L is set to zero. Secondly, the microscopic theory is independent of the conveniently chosen macroscopic scale of length k. The freedom of choice of k is exploited along with the assumed renormalizability of the theory to provide the renormalization group equations which directly imply the universal scaling laws for macroscopic properties. The renormalizability of the model implies the existence of the general relations between the basic macroparameters, such as chain length, excluded volume, etc., and their microscopic counterparts in the microscopic model for the system. These macro--micro relations are defined through the condition that macroscopic quantities be well defined for polymer chains for any spatial dimensionality. The method is illustrated by calculating the end vector distribution function for all values of end vectors R. The evaluation of this distribution function currently requires the use of expansions in e = 4-d. In this case our distribution reduces to known limits for R→0 or infinity. Subsequent papers will present calculations of the polymer coherent scattering function, the monomer spatial distribution function, and concentration dependent properties

Non-perturbative quark mass renormalization

CERN Document Server

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

1998-01-01

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

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

Effects of Random Environment on a Self-Organized Critical System: Renormalization Group Analysis of a Continuous Model

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Antonov N.V.

2016-01-01

Full Text Available We study effects of the random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝ δ(t − t′/k⊥d-1+ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to a certain preferred direction – the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa–Kardar model is irrelevant and to the “pure” Hwa–Kardar model (the advection is irrelevant. For the special case ξ = 2(4 − d/3 both the nonlinearity and the advection are important. The corresponding critical exponents are found exactly for all these cases.

Supersymmetric renormalization prescription in N=4 super-Yang-Mills theory

International Nuclear Information System (INIS)

Baulieu, Laurent; Bossard, Guillaume

2006-01-01

Using the shadow dependent decoupled Slavnov-Taylor identities associated to gauge invariance and supersymmetry, we discuss the renormalization of the N=4 super-Yang-Mills theory and of its coupling to gauge-invariant operators. We specify the method for the determination of non-supersymmetric counterterms that are needed to maintain supersymmetry

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.

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.

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...

Deviations from scale invariance near a general conformal background

International Nuclear Information System (INIS)

Babichenko, A.; Elitzur, S.

1994-01-01

Deviations from scale invariance resulting from small perturbations of a general two-dimensional conformal field theory are studied. They are expressed in terms of β-functions for the renormalization of general couplings under a local change of scale. The β-functions for a homogeneous background are given perturbatively in terms of the data of the original conformal theory without any specific assumptions on its nature. The renormalization of couplings to primary operators and to first descendents is considered as well as that of couplings of a dilatonic type which involve explicit dependence on world sheet curvature. The first descendent couplings are interpreted as gauge degrees of freedom in the string field action and the corresponding gauge transformation is spelled out. (orig.)

Holographic renormalization and supersymmetry

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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.

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.

Dynamical renormalization group approach to transport in ultrarelativistic plasmas: The electrical conductivity in high temperature QED

International Nuclear Information System (INIS)

Boyanovsky, Daniel; Vega, Hector J. de; Wang Shangyung

2003-01-01

The dc electrical conductivity of an ultrarelativistic QED plasma is studied in real time by implementing the dynamical renormalization group. The conductivity is obtained from the real-time dependence of a dissipative kernel closely related to the retarded photon polarization. Pinch singularities in the imaginary part of the polarization are manifest as secular terms that grow in time in the perturbative expansion of this kernel. The leading secular terms are studied explicitly and it is shown that they are insensitive to the anomalous damping of hard fermions as a result of a cancellation between self-energy and vertex corrections. The resummation of the secular terms via the dynamical renormalization group leads directly to a renormalization group equation in real time, which is the Boltzmann equation for the (gauge invariant) fermion distribution function. A direct correspondence between the perturbative expansion and the linearized Boltzmann equation is established, allowing a direct identification of the self-energy and vertex contributions to the collision term. We obtain a Fokker-Planck equation in momentum space that describes the dynamics of the departure from equilibrium to leading logarithmic order in the coupling. This equation determines that the transport time scale is given by t tr =24 π/e 4 T ln(1/e). The solution of the Fokker-Planck equation approaches asymptotically the steady-state solution as ∼e -t/(4.038...t tr ) . The steady-state solution leads to the conductivity σ=15.698 T/e 2 ln(1/e) to leading logarithmic order. We discuss the contributions beyond leading logarithms as well as beyond the Boltzmann equation. The dynamical renormalization group provides a link between linear response in quantum field theory and kinetic theory

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)

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 of NN scattering: Contact potential

International Nuclear Information System (INIS)

Yang Jifeng; Huang Jianhua

2005-01-01

The renormalization of the T matrix for NN scattering with a contact potential is re-examined in a nonperturbative regime through rigorous nonperturbative solutions. Based on the underlying theory, it is shown that the ultraviolet divergences in the nonperturbative solutions of the T matrix should be subtracted through 'endogenous' counterterms, which in turn leads to a nontrivial prescription dependence. Moreover, employing the effective range expansion, the importance of imposing physical boundary conditions to remove the nontrivial prescription dependence, especially before making any physical claims, is discussed and highlighted. As by-products, some relations between the effective range expansion parameters are derived. We also discuss the power counting of the couplings for the nucleon-nucleon interactions and other subtle points related to the EFT framework beyond perturbative treatment

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

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

Dressed skeleton expansion and the coupling scale ambiguity problem

International Nuclear Information System (INIS)

Lu, Hung Jung.

1992-09-01

Perturbative expansions in quantum field theories are usually expressed in powers of a coupling constant. In principle, the infinite sum of the expansion series is independent of the renormalization scale of the coupling constant. In practice, there is a remnant dependence of the truncated series on the renormalization scale. This scale ambiguity can severely restrict the predictive power of theoretical calculations. The dressed skeleton expansion is developed as a calculational method which avoids the coupling scale ambiguity problem. In this method, physical quantities are expressed as functional expansions in terms of a coupling vertex function. The arguments of the vertex function are given by the physical momenta of each process. These physical momenta effectively replace the unspecified renormalization scale and eliminate the ambiguity problem. This method is applied to various field theoretical models and its main features and limitations are explored. For quantum chromodynamics, an expression for the running coupling constant of the three-gluon vertex is obtained. The effective coupling scale of this vertex is shown to be essentially given by μ 2 ∼ Q min 2 Q med 2 /Q max 2 where Q min 2 Q med 2 /Q max 2 are respectively the smallest, the next-to-smallest and the largest scale among the three gluon virtualities. This functional form suggests that the three-gluon vertex becomes non-perturbative at asymmetric momentum configurations. Implications for four-jet physics is 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

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.)

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

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.

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

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.

The effective potential in the presence of several mass scales

International Nuclear Information System (INIS)

Casas, J.A.; Di Clemente, V.; Quiros, M.

1999-01-01

We consider the problem of improving the effective potential in mass independent schemes, as e.g. the MS-bar or DR-bar renormalization scheme, in the presence of an arbitrary number of fields with PHI-dependent masses M i(PHI c ) . We use the decoupling theorem at the scales μ i M i (PHI c ) such that the matching between the effective (low energy) and complete (high energy) one-loop theories contains no thresholds. We find that for any value of PHI c , there is a convenient scale μ * ≡ min i M i (PHI c ), at which the loop expansion has the best behaviour and the effective potential has the least μ-dependence. Furthermore, at this scale the effective potential coincides with the (improved) tree-level one in the effective field theory. The decoupling method is explicitly illustrated with a simple Higgs-Yukawa model, along with its relationship with other decoupling prescriptions and with proposed multi-scale renormalization approaches. The procedure leads to a nice suppression of potentially large logarithms and can be easily adapted to include higher-loop effects, which is explicitly shown at the two-loop level

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

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.

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

Renormalization-group theory of spinodal decomposition

International Nuclear Information System (INIS)

Mazenko, G.F.; Valls, O.T.; Zhang, F.C.

1985-01-01

Renormalization-group (RG) methods developed previously for the study of the growth of order in unstable systems are extended to treat the spinodal decomposition of the two-dimensional spin-exchange kinetic Ising model. The conservation of the order parameter and fixed-length sum rule are properly preserved in the theory. Various correlation functions in both coordinate and momentum space are calculated as functions of time. The scaling function for the structure factor is extracted. We compare our results with direct Monte Carlo (MC) simulations and find them in good agreement. The time rescaling parameter entering the RG analysis is temperature dependent, as was determined in previous work through a RG analysis of MC simulations. The results exhibit a long-time logarithmic growth law for the typical domain size, both analytically and numerically. In the time region where MC simulations have previously been performed, the logarithmic growth law can be fitted to a power law with an effective exponent. This exponent is found to be in excellent agreement with the result of MC simulations. The logarithmic growth law agrees with a physical model of interfacial motion which involves an interplay between the local curvature and an activated jump across the interface

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

International Nuclear Information System (INIS)

Grap, Stephan Michael

2013-01-01

We studied the influence of spin-orbit interaction (SOI) in interacting low dimensional quantum systems at zero temperature within the framework of the functional renormalization group (fRG). Among the several types of spin-orbit interaction the so-called Rashba spin-orbit interaction is especially intriguing for future spintronic applications as it may be tuned via external electric fields. We investigated its effect on the low energy physics of an interacting quantum wire in an applied Zeeman field which is modeled as a generalization of the extended Hubbard model. To this end we performed a renormalization group study of the two particle interaction, including the SOI and the Zeeman field exactly on the single particle level. Considering the resulting two band model, we formulated the RG equations for the two particle vertex keeping the full band structure as well as the non trivial momentum dependence of the low energy two particle scattering processes. In order to solve these equations numerically we defined criteria that allowed us to classify whether a given set of initial conditions flows towards the strongly coupled regime. We found regions in the models parameter space where a weak coupling method as the fRG is applicable and it is possible to calculate additional quantities of interest. Furthermore we analyzed the effect of the Rashba SOI on the properties of an interacting multi level quantum dot coupled to two semi in nite leads. Of special interest was the interplay with a Zeeman field and its orientation with respect to the SOI term. We found a renormalization of the spin-orbit energy which is an experimental quantity used to asses SOI effects in transport measurements, as well as renormalized effective g factors used to describe the Zeeman field dependence. In particular in asymmetrically coupled systems the large parameter space allows for rich physics which we studied by means of the linear conductance obtained via the generalized Landauer

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.)

Quantum gravity at a TeV and the renormalization of Newton's constant

International Nuclear Information System (INIS)

Calmet, Xavier; Hsu, Stephen D. H.; Reeb, David

2008-01-01

We examine whether renormalization effects can cause Newton's constant to change dramatically with energy, perhaps even reducing the scale of quantum gravity to the TeV region without the introduction of extra dimensions. We examine a model that realizes this possibility and describe experimental signatures from the production of small black holes

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.)

Scale separation closure and Alfven wave turbulence

International Nuclear Information System (INIS)

Chen, C.Y.; Mahajan, S.M.

1985-04-01

Based on the concept of scale separation between coherent response function and incoherent source for renormalized turbulence theories, a closure scheme is proposed. A model problem dealing with shear-Alfven wave turbulence is numerically solved; the solution explicitly shows expected turbulence features such as frequency shift from linear modes, band-broadening, and a power law dependence for the turbulence spectrum

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

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 ...

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)

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

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.

Renormalizations and operator expansion in sigma model

International Nuclear Information System (INIS)

Terentyev, M.V.

1988-01-01

The operator expansion (OPE) is studied for the Green function at x 2 → 0 (n(x) is the dynamical field ofσ-model) in the framework of the two-dimensional σ-model with the O(N) symmetry group at large N. As a preliminary step we formulate the renormalization scheme which permits introduction of an arbitrary intermediate scale μ 2 in the framework of 1/N expansion and discuss factorization (separation) of small (p μ) momentum region. It is shown that definition of composite local operators and coefficient functions figuring in OPE is unambiguous only in the leading order in 1/N expansion when dominant are the solutions with extremum of action. Corrections of order f(μ 2 )/N (here f(μ 2 ) is the effective interaction constant at the point μ 2 ) in composite operators and coefficient functions essentially depend on factorization method of high and low momentum regions. It is shown also that contributions to the power corrections of order m 2 x 2 f(μ 2 )/N in the Green function (here m is the dynamical mass-scale factor in σ-model) arise simultaneously from two sources: from the mean vacuum value of the composite operator n ∂ 2 n and from the hard particle contributions in the coefficient function of unite operator. Due to the analogy between σ-model and QCD the obtained result indicates theoretical limitations to the sum rule method in QCD. (author)

Renormalization group and finite size effects in scalar lattice field theories

International Nuclear Information System (INIS)

Bernreuther, W.; Goeckeler, M.

1988-01-01

Binder's phenomenological renormalization group is studied in the context of the O(N)-symmetric euclidean lattice φ 4 theory in dimensions d ≤ 4. By means of the field theoretical formulation of the renormalization group we analyse suitable ratios of Green functions on finite lattices in the limit where the dimensionless lattice length L >> 1 and where the dimensionless bare mass approaches the critical point of the corresponding infinite volume model. If the infrared-stable fixed point which controls this limit is a simple zero of the β-function we are led to formulae which allow the extraction of the critical exponents ν and η. For the gaussian fixed point in four dimensions, discussed as a known example for a multiple zero of the β-function, we derive for these ratios the leading logarithmic corrections to mean field scaling. (orig.)

Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity

Science.gov (United States)

Toniato, Júnior D.; Rodrigues, Davi C.; de Almeida, Álefe O. F.; Bertini, Nicolas

2017-09-01

We apply the full Will-Nordtvedt version of the parametrized post-Newtonian (PPN) formalism to a class of general relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant G is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the external potential effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales; for any of them the Solar System bounds need to be considered.

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

Renormalization theory of beam-beam interaction in electron-positron colliders

International Nuclear Information System (INIS)

Chin, Y.H.

1989-07-01

This note is devoted to explaining the essence of the renormalization theory of beam-beam interaction for carrying out analytical calculations of equilibrium particle distributions in electron-positron colliding beam storage rings. Some new numerical examples are presented such as for betatron tune dependence of the rms beam size. The theory shows reasonably good agreements with the results of computer simulations. 5 refs., 6 figs

On the Renormalization of the Effective Field Theory of Large Scale Structures

OpenAIRE

Pajer, Enrico; Zaldarriaga, Matias

2013-01-01

Standard perturbation theory (SPT) for large-scale matter inhomogeneities is unsatisfactory for at least three reasons: there is no clear expansion parameter since the density contrast is not small on all scales; it does not fully account for deviations at large scales from a perfect pressureless fluid induced by short-scale non-linearities; for generic initial conditions, loop corrections are UV-divergent, making predictions cutoff dependent and hence unphysical. The Effective Field Theory o...

Matrix-dependent multigrid-homogenization for diffusion problems

Energy Technology Data Exchange (ETDEWEB)

Knapek, S. [Institut fuer Informatik tu Muenchen (Germany)

1996-12-31

We present a method to approximately determine the effective diffusion coefficient on the coarse scale level of problems with strongly varying or discontinuous diffusion coefficients. It is based on techniques used also in multigrid, like Dendy`s matrix-dependent prolongations and the construction of coarse grid operators by means of the Galerkin approximation. In numerical experiments, we compare our multigrid-homogenization method with homogenization, renormalization and averaging approaches.

Gauge invariance and holographic renormalization

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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.

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.

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.

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

Renormalization of QED with planar binary trees

International Nuclear Information System (INIS)

Brouder, C.

2001-01-01

The Dyson relations between renormalized and bare photon and electron propagators Z 3 anti D(q)=D(q) and Z 2 anti S(q)=S(q) are expanded over planar binary trees. This yields explicit recursive relations for the terms of the expansions. When all the trees corresponding to a given power of the electron charge are summed, recursive relations are obtained for the finite coefficients of the renormalized photon and electron propagators. These relations significantly decrease the number of integrals to carry out, as compared to the standard Feynman diagram technique. In the case of massless quantum electrodynamics (QED), the relation between renormalized and bare coefficients of the perturbative expansion is given in terms of a Hopf algebra structure. (orig.)

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)

Non-perturbative renormalization of the static vector current and its O(a)-improvement in quenched QCD

Energy Technology Data Exchange (ETDEWEB)

Palombi, F.

2007-06-15

We carry out the renormalization and the Symanzik O(a)-improvement programme for the static vector current in quenched lattice QCD. The scale independent ratio of the renormalization constants of the static vector and axial currents is obtained non-perturbatively from an axial Ward identity with Wilson-type light quarks and various lattice discretizations of the static action. The improvement coefficients c{sub V}{sup stat} and b{sub V}{sup stat} are obtained up to O(g{sub 4}{sup 0})-terms by enforcing improvement conditions respectively on the axial Ward identity and a three-point correlator of the static vector current. A comparison between the non-perturbative estimates and the corresponding one-loop results shows a non-negligible effect of the O(g{sub 4}{sup 0})-terms on the improvement coefficients but a good accuracy of the perturbative description of the ratio of the renormalization constants. (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.

Structural vs electronic origin of renormalized band widths in TTF-TCNQ: An angular dependent NEXAFS study

DEFF Research Database (Denmark)

Sing, M; Meyer, J; Hoinkis, M

2007-01-01

in the topmost surface layer. We find that the tilt angles of the molecules with respect to the one-dimensional axis are essentially the same as in the bulk. Thus, we can rule out surface relaxation as the origin of the renormalized band widths which were inferred from the analysis of photoemission data within...

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.

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.

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.)

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

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

Renormalization group evolution of the universal theories EFT

International Nuclear Information System (INIS)

Wells, James D.; Zhang, Zhengkang

2016-01-01

The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.

Calculated dependence of FePt damping on external field magnitude and direction

Directory of Open Access Journals (Sweden)

N. A. Natekar

2017-05-01

Full Text Available Near the Curie temperature (Tc, magnetic parameters including magnetization, anisotropy, and damping depend strongly on both temperature and length scale. This manifestation of renormalization theory is most readily seen in the case of magnetization where the magnitude of the atomic spin is largely unaffected by temperature, but the bulk magnetization vanishes at Tc. It has been previously argued that the Landau-Lifshitz-Gilbert damping parameter alpha exhibits a similar effect owing to its dependence on both atomic effects and magnon-magnon scattering, the latter having a strong length dependence. Here, we calculate, using an anisotropic exchange description of L10 FePt (Tc = 705 K, the damping (and other magnetic properties dependence on temperature for FePt at length scales around 1.0 nm as appropriate for high temperature micromagnetic simulation. While the damping reduces as the applied field along the easy direction increases, it tends to increase as the field direction is changed to in-plane. The renormalized parameters are also calculated for higher and lower Tc (770K and 630K by invoking the linear relationship between the exchange stiffness parameter and Curie temperature. This corresponds to doped and/or non-stoichiometric FePt and allows better understanding of the effects of varying anisotropy to exchange ratio.

Scaling of the first-passage time of biased diffusion on hierarchical comb structures

International Nuclear Information System (INIS)

Lin Zhifang; Tao Ruibao.

1989-12-01

Biased diffusion on hierarchical comb structures is studied within an exact renormalization group scheme. The scaling exponents of the moments of the first-passage time for random walks are obtained. It is found that the scaling properties of the diffusion depend only on the direction of bias. In this particular case, the presence of bias may give rise to a new multifractality. (author). 7 refs, 2 figs

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...

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

Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)

Science.gov (United States)

Lahoche, Vincent; Oriti, Daniele

2017-01-01

We study the renormalization of a general field theory on the homogeneous space (SU(2)/ ≤ft. U(1)\\right){{}× d} with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power counting for arbitrary d. For the case d  =  4, we prove perturbative renormalizability to all orders via multi-scale analysis, study both the renormalized and effective perturbation series, and establish the asymptotic freedom of the model. We also outline a general power counting for the homogeneous space {{≤ft(SO(D)/SO(D-1)\\right)}× d} , of direct interest for quantum gravity models in arbitrary dimension, and point out the obstructions to the direct generalization of our results to these cases.

Scaling symmetry, renormalization, and time series modeling: the case of financial assets dynamics.

Science.gov (United States)

Zamparo, Marco; Baldovin, Fulvio; Caraglio, Michele; Stella, Attilio L

2013-12-01

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.

Scaling symmetry, renormalization, and time series modeling: The case of financial assets dynamics

Science.gov (United States)

Zamparo, Marco; Baldovin, Fulvio; Caraglio, Michele; Stella, Attilio L.

2013-12-01

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments’ stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.

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

Exact renormalization group equation for the Lifshitz critical point

Science.gov (United States)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

A renormalization group study of persistent current in a quasiperiodic ring

Energy Technology Data Exchange (ETDEWEB)

Dutta, Paramita [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India); Maiti, Santanu K., E-mail: santanu.maiti@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata-700 108 (India); Karmakar, S.N. [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India)

2014-04-01

We propose a real-space renormalization group approach for evaluating persistent current in a multi-channel quasiperiodic Fibonacci tight-binding ring based on a Green's function formalism. Unlike the traditional methods, the present scheme provides a powerful tool for the theoretical description of persistent current with a very high degree of accuracy in large periodic and quasiperiodic rings, even in the micron scale range, which emphasizes the merit of this work.

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.

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 in self-consistent approximation schemes at finite temperature I: theory

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2001-07-01

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)

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.)

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)

Scaling versus asymptotic scaling in the non-linear σ-model in 2D. Continuum version

International Nuclear Information System (INIS)

Flyvbjerg, H.

1990-01-01

The two-point function of the O(N)-symmetric non-linear σ-model in two dimensions is large-N expanded and renormalized, neglecting terms of O(1/N 2 ). At finite cut-off, universal, analytical expressions relate the magnetic susceptibility and the dressed mass to the bare coupling. Removing the cut-off, a similar relation gives the renormalized coupling as a function of the mass gap. In the weak-coupling limit these relations reproduce the results of renormalization group improved weak-coupling perturbation theory to two-loop order. The constant left unknown, when the renormalization group is integrated, is determined here. The approach to asymptotic scaling is studied for various values of N. (orig.)

Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts.

Science.gov (United States)

Grzywacz, Piotr; Qin, Jian; Morse, David C

2007-12-01

Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, i.e., by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor S(-1)(k) predicted by a "one-loop" approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of an UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to S(-1)(k) is shown to be the sum of (i) a k -independent contribution that arises from a renormalization of the effective chi parameter, (ii) a k-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to k(2) that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a k-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.

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.

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.

Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model

Energy Technology Data Exchange (ETDEWEB)

Meloni, Davide [Dipartimento di Matematica e Fisica, Università di Roma Tre,Via della Vasca Navale 84, 00146 Rome (Italy); Ohlsson, Tommy; Riad, Stella [Department of Physics, School of Engineering Sciences,KTH Royal Institute of Technology - AlbaNova University Center,Roslagstullsbacken 21, 106 91 Stockholm (Sweden)

2017-03-08

We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10{sub H}, 120{sub H}, and 126{sub H} representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M{sub I}. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10{sub H} and 126{sub H} representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.

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.

Interactions of disparate scales in drift-wave turbulence

International Nuclear Information System (INIS)

Krommes, John A.; Kim, Chang-Bae

2000-01-01

Renormalized statistical theory is used to calculate the interactions between short scales (wave vector k) and long scales (wave vector q parallel =0 fluctuations). The calculations include the zonal-flow growth rate as a special case, but also describe long-wavelength fluctuations with q oriented at an arbitrary angle to the background gradient. The results are fully renormalized. They are subtly different from those of previous authors, in both mathematical form and physical interpretation. A term arising in previous treatments that is related to the propagation of short-scale wave packets is shown to be a higher-order effect that must consistently be neglected to lowest order in a systematic expansion in q/k. Rigorous functional methods are used to show that the long-wavelength growth rate γ q is related to second-order functional variations of the short-wavelength energy and to derive a heuristic algorithm. The principal results are recovered from simple estimates involving the first-order wave-number distension rate tilde γ k (1) dot eqdot kdeltilde Omega k /k 2 , where tilde Ω k is a nonlinear random advection frequency. Fokker-Planck analysis involving tilde γ k (1) is used to heuristically recover the evolution equation for the small scales, and a random-walk flux argument that relates tilde γ k (1) to an effective autocorrelation time is used to give an independent calculation of γ q . Both the rigorous and heuristic derivations demonstrate that the results do not depend on, and cannot be derived from, properties of linear normal modes; they are intrinsically nonlinear. The importance of random-Galilean-invariant renormalization is stressed

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

Scale-Dependent Grasp

OpenAIRE

Kaneko, Makoto; Shirai, Tatsuya; Tsuji, Toshio

2000-01-01

This paper discusses the scale-dependent grasp.Suppose that a human approaches an object initially placed on atable and finally achieves an enveloping grasp. Under such initialand final conditions, he (or she) unconsciously changes the graspstrategy according to the size of objects, even though they havesimilar geometry. We call the grasp planning the scale-dependentgrasp. We find that grasp patterns are also changed according tothe surface friction and the geometry of cross section in additi...

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 group approach to soft gluon resummation

International Nuclear Information System (INIS)

Forte, Stefano; Ridolfi, Giovanni

2003-01-01

We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single dimensionful variable, and then using the renormalization group to resum them. Beyond the next-to-leading log level, our result is somewhat less predictive than previous all-order resummation formulae, but it does not rely on non-standard factorization, and it is thus possibly more general. We use our result to settle issues of convergence of the resummed series, we discuss scheme dependence at the resummed level, and we provide explicit resummed expressions in various factorization schemes

Scaling solutions for dilaton quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Henz, T.; Pawlowski, J.M., E-mail: j.pawlowski@thphys.uni-heidelberg.de; Wetterich, C.

2017-06-10

Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale k is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of k. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.

Towards a taxonomy of spatial scale-dependence

DEFF Research Database (Denmark)

Sandel, Brody Steven

2015-01-01

Spatial scale-dependence is a ubiquitous feature of ecological systems. This presents a challenge for ecologists who seek to discern general principles. A solution is to search for generalities in patterns of scale-dependence – that is, what kinds of things are scale-dependent, in what ways, and ...

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.

Scale-invariant feature extraction of neural network and renormalization group flow

Science.gov (United States)

Iso, Satoshi; Shiba, Shotaro; Yokoo, Sumito

2018-05-01

Theoretical understanding of how a deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse graining. It reminds us of the basic renormalization group (RG) concept in statistical physics. In order to explore possible relations between DNN and RG, we use the restricted Boltzmann machine (RBM) applied to an Ising model and construct a flow of model parameters (in particular, temperature) generated by the RBM. We show that the unsupervised RBM trained by spin configurations at various temperatures from T =0 to T =6 generates a flow along which the temperature approaches the critical value Tc=2.2 7 . This behavior is the opposite of the typical RG flow of the Ising model. By analyzing various properties of the weight matrices of the trained RBM, we discuss why it flows towards Tc and how the RBM learns to extract features of spin configurations.

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method.

Science.gov (United States)

Yao, Yao; Sun, Ke-Wei; Luo, Zhen; Ma, Haibo

2018-01-18

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

The renormalization group study of the effective theory of lattice QED

International Nuclear Information System (INIS)

Sugiyama, Y.

1988-01-01

The compact U(1) lattice gauge theory with massless fermions (Lattice QED) is studied through the effective model analytically, using the renormalization group method. The obtained effective model is the local boson field system with non-local interactions. The authors study the existence of non-trivial fixed point and its scaling behavior. This fixed point seems to be tri-critical. Such fixed point is interpreted in terms of the original Lattice QED model, and the results are consistent with the Monte Calro study

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.

Renormalization of weak noises of arbitrary shape for one-dimensional critical dynamical systems Announcement of results and numerical explorations

CERN Document Server

Diaz-Espinosa, O

2006-01-01

We study the effect of noise on one--dimensional critical dynamical systems (that is, maps with a renormalization theory). We consider in detail two examples of such dynamical systems: unimodal maps of the interval at the accumulation of period--doubling and smooth homeomorphisms of the circle with a critical point and with golden mean rotation number. We show that, if we scale the space and the time, several properties of the noise (the cumulants or Wick--ordered moments) satisfy some scaling relations. A consequence of the scaling relations is that a version of the central limit theorem holds. Irrespective of the shape of the initial noise, if the bare noise is weak enough, the effective noise becomes close to Gaussian in several senses that we can make precise. We notice that the conclusions are false for maps with positive Lyapunov exponents. The method of analysis is close in spirit to the study of scaling limits in renormalization theory. We also perform several numerical experiments that confirm the ri...

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)

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)

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.)

Coexistence of Velocity Renormalization and Ferrimagnetic Fluctuation in the Organic Dirac Electron System α-(BEDT-TTF)2I3

Science.gov (United States)

Matsuno, Genki; Kobayashi, Akito

2018-05-01

We evaluate the uniform spin susceptibility in an extended Hubbard model describing α-(BEDT-TTF)2I3. Employing the Fock-type self-energy with the long-range Coulomb interaction and the random phase approximation with the on-site Coulomb interaction, it is clarified that the characteristic energy scales at which ferrimagnetic fluctuation and velocity renormalization emerge are different. This is why these phenomena coexist while the ferrimagnetic fluctuation is disturbed by the velocity renormalization. In addition, it is found that screening effect to the self-energy is irrelevant in the presence of a strong on-site Coulomb interaction U.

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.)

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

Scaling and crossover in a fermion-boson mixture

International Nuclear Information System (INIS)

Singh, K.K.

1987-01-01

Thermodynamic behaviour of a mixture of weakly interacting fermions and bosons is investigated in (4 - ε) dimensions by the renormalization group method with a view to study scaling and crossover properties of the system in the tricritical region. Conventional tricritical scaling, first found to breakdown for a classical infinite-component model, is seen to do so more spectacularly in the case of the mixture. Whereas in the infinite-component model, conventional scaling holds in the ordered and disordered phases separately (i.e. with different tricritical exponents), no such thing is possible in either of the phases of the mixture. The breakdown of scaling in the mixture is associated with the dimensionless strength v 6 of the 6-point interaction in the effective Hamiltonian which causes the parameters of the renormalized Hamiltonian to depend on two combinations of scaling fields rather than one. The strength v 6 is a quantum mechanical parameter being proportional in 3 dimensions to (b 3 /λ T 4 K F ) where λ T , K F and b denote, respectively, the boson thermal wavelength, the Fermi momentum of the fermion component and the scattering length associated with the fermion-boson interaction. The square root of this quantity agrees with the non-universality parameter which was found to characterize tricritical amplitude ratios in 3 dimensions in an earlier work. (author). 19 refs, 8 figs

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

Renormalization of Fermi Velocity in a Composite Two Dimensional Electron Gas

Science.gov (United States)

Weger, M.; Burlachkov, L.

We calculate the self-energy Σ(k, ω) of an electron gas with a Coulomb interaction in a composite 2D system, consisting of metallic layers of thickness d ≳ a0, where a0 = ħ2ɛ1/me2 is the Bohr radius, separated by layers with a dielectric constant ɛ2 and a lattice constant c perpendicular to the planes. The behavior of the electron gas is determined by the dimensionless parameters kFa0 and kFc ɛ2/ɛ1. We find that when ɛ2/ɛ1 is large (≈5 or more), the velocity v(k) becomes strongly k-dependent near kF, and v(kF) is enhanced by a factor of 5-10. This behavior is similar to the one found by Lindhard in 1954 for an unscreened electron gas; however here we take screening into account. The peak in v(k) is very sharp (δk/kF is a few percent) and becomes sharper as ɛ2/ɛ1 increases. This velocity renormalization has dramatic effects on the transport properties; the conductivity at low T increases like the square of the velocity renormalization and the resistivity due to elastic scattering becomes temperature dependent, increasing approximately linearly with T. For scattering by phonons, ρ ∝ T2. Preliminary measurements suggest an increase in vk in YBCO very close to kF.

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 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

Gauge mediation scenario with hidden sector renormalization in MSSM

International Nuclear Information System (INIS)

Arai, Masato; Kawai, Shinsuke; Okada, Nobuchika

2010-01-01

We study the hidden sector effects on the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5+5 minimal gauge-mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that a stau can be the next lightest superparticle for moderate values of hidden sector self-coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, which imply distinctive signals in ongoing and upcoming collider experiments.

Gauge mediation scenario with hidden sector renormalization in MSSM

Science.gov (United States)

Arai, Masato; Kawai, Shinsuke; Okada, Nobuchika

2010-02-01

We study the hidden sector effects on the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5+5¯ minimal gauge-mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that a stau can be the next lightest superparticle for moderate values of hidden sector self-coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, which imply distinctive signals in ongoing and upcoming collider experiments.

Out-of-equilibrium dynamics driven by localized time-dependent perturbations at quantum phase transitions

Science.gov (United States)

Pelissetto, Andrea; Rossini, Davide; Vicari, Ettore

2018-03-01

We investigate the quantum dynamics of many-body systems subject to local (i.e., restricted to a limited space region) time-dependent perturbations. If the system crosses a quantum phase transition, an off-equilibrium behavior is observed, even for a very slow driving. We show that, close to the transition, time-dependent quantities obey scaling laws. In first-order transitions, the scaling behavior is universal, and some scaling functions can be computed exactly. For continuous transitions, the scaling laws are controlled by the standard critical exponents and by the renormalization-group dimension of the perturbation at the transition. Our protocol can be implemented in existing relatively small quantum simulators, paving the way for a quantitative probe of the universal off-equilibrium scaling behavior, without the need to manipulate systems close to the thermodynamic limit.

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.

Electroweak vacuum instability and renormalized Higgs field vacuum fluctuations in the inflationary universe

Energy Technology Data Exchange (ETDEWEB)

Kohri, Kazunori [Institute of Particle and Nuclear Studies, KEK, 1-1 Oho, Tsukuba 305-0801 (Japan); Matsui, Hiroki, E-mail: kohri@post.kek.jp, E-mail: matshiro@post.kek.jp [The Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba 305-0801 (Japan)

2017-08-01

In this work, we investigated the electroweak vacuum instability during or after inflation. In the inflationary Universe, i.e., de Sitter space, the vacuum field fluctuations < δ φ {sup 2} > enlarge in proportion to the Hubble scale H {sup 2}. Therefore, the large inflationary vacuum fluctuations of the Higgs field < δ φ {sup 2} > are potentially catastrophic to trigger the vacuum transition to the negative-energy Planck-scale vacuum state and cause an immediate collapse of the Universe. However, the vacuum field fluctuations < δ φ {sup 2} >, i.e., the vacuum expectation values have an ultraviolet divergence, and therefore a renormalization is necessary to estimate the physical effects of the vacuum transition. Thus, in this paper, we revisit the electroweak vacuum instability from the perspective of quantum field theory (QFT) in curved space-time, and discuss the dynamical behavior of the homogeneous Higgs field φ determined by the effective potential V {sub eff}( φ ) in curved space-time and the renormalized vacuum fluctuations < δ φ {sup 2} >{sub ren} via adiabatic regularization and point-splitting regularization. We simply suppose that the Higgs field only couples the gravity via the non-minimal Higgs-gravity coupling ξ(μ). In this scenario, the electroweak vacuum stability is inevitably threatened by the dynamical behavior of the homogeneous Higgs field φ, or the formations of AdS domains or bubbles unless the Hubble scale is small enough H < Λ {sub I} .

Renormalization group equation for interacting Thirring fields in dimensional regularization scheme

International Nuclear Information System (INIS)

Chowdhury, A.R.; Roy, T.; Kar, S.

1976-01-01

The dynamics of two interacting Thirring fields has been investigated within the dimensional regularization framework. The coupling constants are renormalized in the same way as observed in the non-perturbative approach of Ansel'm et al (Sov. Phys. - JETP 36: 608 (1959)). Functionsβsub(i)(g 1 , g 2 , g 3 ) and γsub(i)(g 1 , g 2 , g 3 ), pertaining to the stability and anomalous behaviour of the problem, are computed up to a third order in the coupling parameters. With the help of these, subsidiary non-linear differential equations of the renormalization group are studied in 2-epsilon dimension. The results show up some peculiar features of the theory: a zero of βsub(i)(g 1 , g 2 , g 3 ) corresponding to g 2 approximately α√epsilon, a characteristic of phi theory. The scale invariant limit is reached when g 2 → 0 (i.e. the two Thirring fields are decoupled) and also when g 1 = xg 2 = g 3 , where x is a root of 2x 3 + 2x 2 - 1 = 0. The branch-point zero makes the transition to the epsilon tends to 0 limit non-unique. The anomalous dimensions are obtained and seen to match that of the Dashen-Frishman model (Phys. Lett.; 46B 439 (1973)). The existence of a non-trivial scale invariant limit distinguishes the model from many simple field theories. (author)

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.

Traveling waves and the renormalization group improvedBalitsky-Kovchegov equation

Energy Technology Data Exchange (ETDEWEB)

Enberg, Rikard

2006-12-01

I study the incorporation of renormalization group (RG)improved BFKL kernels in the Balitsky-Kovchegov (BK) equation whichdescribes parton saturation. The RG improvement takes into accountimportant parts of the next-to-leading and higher order logarithmiccorrections to the kernel. The traveling wave front method for analyzingthe BK equation is generalized to deal with RG-resummed kernels,restricting to the interesting case of fixed QCD coupling. The resultsshow that the higher order corrections suppress the rapid increase of thesaturation scale with increasing rapidity. I also perform a "diffusive"differential equation approximation, which illustrates that someimportant qualitative properties of the kernel change when including RGcorrections.

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.)

Classical open-string field theory: A∞-algebra, renormalization group and boundary states

International Nuclear Information System (INIS)

Nakatsu, Toshio

2002-01-01

We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance cut-off scale is introduced by length of open-string strip which appears in the Schwinger representation of open-string propagator. Classical open-string field theory in the title means open-string field theory governed by a classical part of the low energy action. It is obtained by integrating out suitable tree interactions of open-strings and is of non-polynomial type. We study this theory by using the BV formalism. It turns out to be deeply related with deformation theory of A ∞ -algebra. We introduce renormalization group equation of this theory and discuss it from several aspects. It is also discussed that this theory is interpreted as a boundary open-string field theory. Closed-string BRST charge and boundary states of closed-string field theory in the presence of open-string field play important roles

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.

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.

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.)

Application of renormalization group theory to the large-eddy simulation of transitional boundary layers

Science.gov (United States)

Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.

1990-01-01

An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.

Non-ladder extended renormalization group analysis of the dynamical chiral symmetry breaking

Energy Technology Data Exchange (ETDEWEB)

Aoki, Ken-Ichi; Takagi, Kaoru; Terao, Haruhiko; Tomoyose, Masashi [Kanazawa Univ., Inst. for Theoretical Physics, Kanazawa, Ishikawa (Japan)

2000-04-01

The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the non-perturbative renormalization group (NPRG) equations. We employ an approximation scheme beyond 'the ladder', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced in comparison with the ladder approximation, which is phenomenologically favorable. The gauge dependence of the order parameters is reduced significantly in this scheme. (author)

Non-ladder extended renormalization group analysis of the dynamical chiral symmetry breaking

International Nuclear Information System (INIS)

Aoki, Ken-Ichi; Takagi, Kaoru; Terao, Haruhiko; Tomoyose, Masashi

2000-01-01

The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the non-perturbative renormalization group (NPRG) equations. We employ an approximation scheme beyond 'the ladder', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced in comparison with the ladder approximation, which is phenomenologically favorable. The gauge dependence of the order parameters is reduced significantly in this scheme. (author)

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.

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.

The heterogeneous gas with singular interaction: generalized circular law and heterogeneous renormalized energy

International Nuclear Information System (INIS)

Molino, Luis Carlos García del; Pakdaman, Khashayar; Touboul, Jonathan

2015-01-01

We introduce and analyze d-dimensional Coulomb gases with random charge distribution and general external confining potential. We show that these gases satisfy a large-deviation principle. The analysis of the minima of the rate function (which is the leading term of the energy) reveals that, at equilibrium, the particle distribution is a generalized circular law (i.e. with spherical support but not necessarily uniform distribution). In the classical electrostatic external potential, there are infinitely many minimizers of the rate function. The most likely macroscopic configuration is a disordered distribution in which particles are uniformly distributed (for d = 2, the circular law), and charges are independent of the positions of the particles. General charge-dependent confining potentials unfold this degenerate situation: in contrast, the particle density is not uniform, and particles spontaneously organize according to their charge. In this picture the classical electrostatic potential appears as a transition at which order is lost. Sub-leading terms of the energy are derived: we show that these are related to an operator, generalizing the Coulomb renormalized energy, which incorporates the heterogeneous nature of the charges. This heterogeneous renormalized energy informs us about the microscopic arrangements of the particles, which are non-standard, strongly dependent on the charges, and include progressive and irregular lattices. (paper)

Higgs boson, renormalization group, and naturalness in cosmology

International Nuclear Information System (INIS)

Barvinsky, A.O.; Kamenshchik, A.Yu.; Kiefer, C.; Starobinsky, A.A.; Steinwachs, C.F.

2012-01-01

We consider the renormalization group improvement in the theory of the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. At the one-loop level with the running of constants taken into account, it leads to a range of the Higgs mass that is entirely determined by the lower WMAP bound on the cosmic microwave background (CMB) spectral index. We find that the SM phenomenology is sensitive to current cosmological data, which suggests to perform more precise CMB measurements as a SM test complementary to the LHC program. By using the concept of a field-dependent cutoff, we show the naturalness of the gradient and curvature expansion in this model within the conventional perturbation theory range of the SM. We also discuss the relation of these results to two-loop calculations and the limitations of the latter caused by parametrization and gauge dependence problems. (orig.)

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

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.

Influence of anisotropy on anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field.

Science.gov (United States)

Jurcisinová, E; Jurcisin, M; Remecký, R

2009-10-01

The influence of weak uniaxial small-scale anisotropy on the stability of the scaling regime and on the anomalous scaling of the single-time structure functions of a passive scalar advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and operator-product expansion within one-loop approximation of a perturbation theory. The explicit analytical expressions for coordinates of the corresponding fixed point of the renormalization-group equations as functions of anisotropy parameters are found, the stability of the three-dimensional Kolmogorov-like scaling regime is demonstrated, and the dependence of the borderline dimension d(c) is an element of (2,3] between stable and unstable scaling regimes is found as a function of the anisotropy parameters. The dependence of the turbulent Prandtl number on the anisotropy parameters is also briefly discussed. The influence of weak small-scale anisotropy on the anomalous scaling of the structure functions of a passive scalar field is studied by the operator-product expansion and their explicit dependence on the anisotropy parameters is present. It is shown that the anomalous dimensions of the structure functions, which are the same (universal) for the Kraichnan model, for the model with finite time correlations of the velocity field, and for the model with the advection by the velocity field driven by the stochastic Navier-Stokes equation in the isotropic case, can be distinguished by the assumption of the presence of the small-scale anisotropy in the systems even within one-loop approximation. The corresponding comparison of the anisotropic anomalous dimensions for the present model with that obtained within the Kraichnan rapid-change model is done.

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.

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.)

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.)

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.)

Physics in space-time with scale-dependent metrics

Science.gov (United States)

Balankin, Alexander S.

2013-10-01

We construct three-dimensional space Rγ3 with the scale-dependent metric and the corresponding Minkowski space-time Mγ,β4 with the scale-dependent fractal (DH) and spectral (DS) dimensions. The local derivatives based on scale-dependent metrics are defined and differential vector calculus in Rγ3 is developed. We state that Mγ,β4 provides a unified phenomenological framework for dimensional flow observed in quite different models of quantum gravity. Nevertheless, the main attention is focused on the special case of flat space-time M1/3,14 with the scale-dependent Cantor-dust-like distribution of admissible states, such that DH increases from DH=2 on the scale ≪ℓ0 to DH=4 in the infrared limit ≫ℓ0, where ℓ0 is the characteristic length (e.g. the Planck length, or characteristic size of multi-fractal features in heterogeneous medium), whereas DS≡4 in all scales. Possible applications of approach based on the scale-dependent metric to systems of different nature are briefly discussed.

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

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 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

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

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

Perturbative Field-Theoretical Renormalization Group Approach to Driven-Dissipative Bose-Einstein Criticality

Directory of Open Access Journals (Sweden)

Uwe C. Täuber

2014-04-01

Full Text Available The universal critical behavior of the driven-dissipative nonequilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex-valued Landau-Ginzburg functional, which captures the near critical nonequilibrium dynamics, and generalizes model A for classical relaxational dynamics with nonconserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest nontrivial order in the dimensional ε expansion about the upper critical dimension d_{c}=4 and establish the emergence of a novel universal scaling exponent associated with the nonequilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (subdiffusive model B with complex coefficients.

Pole Mass of the W Boson at Two-Loop Order in the Pure $\\overline {MS}$ Scheme

Energy Technology Data Exchange (ETDEWEB)

Martin, Stephen P. [Northern Illinois U.

2015-06-03

I provide a calculation at full two-loop order of the complex pole squared mass of the W boson in the Standard Model in the pure MS¯ renormalization scheme, with Goldstone boson mass effects resummed. This approach is an alternative to earlier ones that use on-shell or hybrid renormalization schemes. The renormalization scale dependence of the real and imaginary parts of the resulting pole mass is studied. Both deviate by about ±4  MeV from their median values as the renormalization scale is varied from 50 to 200 GeV, but the theory error is likely larger. A surprising feature of this scheme is that the two-loop QCD correction has a larger scale dependence, but a smaller magnitude, than the two-loop non-QCD correction, unless the renormalization scale is chosen very far from the top-quark mass.

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

Functional renormalization group study of the Anderson–Holstein model

International Nuclear Information System (INIS)

Laakso, M A; Kennes, D M; Jakobs, S G; Meden, V

2014-01-01

We present a comprehensive study of the spectral and transport properties in the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron–phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson–Holstein quantum dot and find clear signatures of the presence of the phonon mode. (paper)

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.

Critical point phenomena: universal physics at large length scales

International Nuclear Information System (INIS)

Bruce, A.; Wallace, D.

1993-01-01

This article is concerned with the behaviour of a physical system at, or close to, a critical point (ebullition, ferromagnetism..): study of the phenomena displayed in the critical region (Ising model, order parameter, correlation length); description of the configurations (patterns) formed by the microscopic degrees of freedom near a critical point, essential concepts of the renormalization group (coarse-graining, system flow, fixed-point and scale-invariance); how these concepts knit together to form the renormalization group method; and what kind of problems may be resolved by the renormalization group method. 12 figs., 1 ref

Renormalization scheme invariant predictions for deep-inelastic scattering and determination of ΛQCD

International Nuclear Information System (INIS)

Vovk, V.I.

1989-01-01

Theoretical aspects of the renormalization scheme (RS) ambiguity problem and the approaches to its solution are discussed from the point of view of QCD phenomenology and the scale Λ determination. The method of RS-invariant perturbation theory (RSIPT) as a sound basis for describing experiment in QCD is advocated. To this end the method is developed for the non-singlet structure functions (SF) of deep-inelastic scattering and recent high precision data on SF's are analyzed in a RS-invariant way. It is shown that RSIPT leads to a more accurate and reliable determination of the QCD scale Λ, which is consistent with the theoretical assumption of a better convergence of RS-invariant perturbative series. 24 refs.; 1 tab

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.

Numerical renormalization group method for entanglement negativity at finite temperature

Science.gov (United States)

Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.

2018-04-01

We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.

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

Strong-coupling Bose polarons out of equilibrium: Dynamical renormalization-group approach

Science.gov (United States)

Grusdt, Fabian; Seetharam, Kushal; Shchadilova, Yulia; Demler, Eugene

2018-03-01

When a mobile impurity interacts with a surrounding bath of bosons, it forms a polaron. Numerous methods have been developed to calculate how the energy and the effective mass of the polaron are renormalized by the medium for equilibrium situations. Here, we address the much less studied nonequilibrium regime and investigate how polarons form dynamically in time. To this end, we develop a time-dependent renormalization-group approach which allows calculations of all dynamical properties of the system and takes into account the effects of quantum fluctuations in the polaron cloud. We apply this method to calculate trajectories of polarons following a sudden quench of the impurity-boson interaction strength, revealing how the polaronic cloud around the impurity forms in time. Such trajectories provide additional information about the polaron's properties which are challenging to extract directly from the spectral function measured experimentally using ultracold atoms. At strong couplings, our calculations predict the appearance of trajectories where the impurity wavers back at intermediate times as a result of quantum fluctuations. Our method is applicable to a broader class of nonequilibrium problems. As a check, we also apply it to calculate the spectral function and find good agreement with experimental results. At very strong couplings, we predict that quantum fluctuations lead to the appearance of a dark continuum with strongly suppressed spectral weight at low energies. While our calculations start from an effective Fröhlich Hamiltonian describing impurities in a three-dimensional Bose-Einstein condensate, we also calculate the effects of additional terms in the Hamiltonian beyond the Fröhlich paradigm. We demonstrate that the main effect of these additional terms on the attractive side of a Feshbach resonance is to renormalize the coupling strength of the effective Fröhlich model.

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.

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.

Scale dependent inference in landscape genetics

Science.gov (United States)

Samuel A. Cushman; Erin L. Landguth

2010-01-01

Ecological relationships between patterns and processes are highly scale dependent. This paper reports the first formal exploration of how changing scale of research away from the scale of the processes governing gene flow affects the results of landscape genetic analysis. We used an individual-based, spatially explicit simulation model to generate patterns of genetic...

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)

Renormalized second post-Newtonian spin contributions to the accumulated orbital phase for LISA sources

International Nuclear Information System (INIS)

Gergely, Laszlo Arpad; Mikoczi, Balazs

2009-01-01

We give here a new third post-Newtonian (3PN) spin-spin contribution (in the PN parameter ε) to the accumulated orbital phase of a compact binary, arising from the spin-orbit precessional motion of the spins. In the equal mass case, this contribution vanishes, but Laser Interferometer Space Antenna (LISA) sources of merging supermassive binary black holes have typically a mass ratio of 1:10. For such nonequal masses, this 3PN correction is periodic in time, with a period approximately ε -1 times larger than the period of gravitational waves. We derive a renormalized and simpler expression of the spin-spin coefficient at 2PN, as an average over the time scale of this period of the combined 2PN and 3PN contribution. We also find that for LISA sources the quadrupole-monopole contribution to the phase dominates over the spin-spin contribution, while the self-spin contribution is negligible even for the dominant spin. Finally, we define a renormalized total spin coefficient σ to be employed in the search for gravitational waves emitted by LISA sources.

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.

Renormalization group theory impact on experimental magnetism

CERN Document Server

Köbler, Ulrich

2010-01-01

Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are calle...

Non-Perturbative Formulation of Time-Dependent String Solutions

CERN Document Server

Alexandre, J; Mavromatos, Nikolaos E; Alexandre, Jean; Ellis, John; Mavromatos, Nikolaos E.

2006-01-01

We formulate here a new world-sheet renormalization-group technique for the bosonic string, which is non-perturbative in the Regge slope alpha' and based on a functional method for controlling the quantum fluctuations, whose magnitudes are scaled by the value of alpha'. Using this technique we exhibit, in addition to the well-known linear-dilaton cosmology, a new, non-perturbative time-dependent background solution. Using the reparametrization invariance of the string S-matrix, we demonstrate that this solution is conformally invariant to alpha', and we give a heuristic inductive argument that conformal invariance can be maintained to all orders in alpha'. This new time-dependent string solution may be applicable to primordial cosmology or to the exit from linear-dilaton cosmology at large times.

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)

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.

Origins of scaling relations in nonequilibrium growth

International Nuclear Information System (INIS)

Escudero, Carlos; Korutcheva, Elka

2012-01-01

Scaling and hyperscaling laws provide exact relations among critical exponents describing the behavior of a system at criticality. For nonequilibrium growth models with a conserved drift, there exist few of them. One such relation is α + z = 4, found to be inexact in a renormalization group calculation for several classical models in this field. Herein, we focus on the two-dimensional case and show that it is possible to construct conserved surface growth equations for which the relation α + z = 4 is exact in the renormalization group sense. We explain the presence of this scaling law in terms of the existence of geometric principles dominating the dynamics. (paper)

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.)

Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids

International Nuclear Information System (INIS)

Meden, V; Schoeller, H; Andergassen, S; Enss, T; Schoenhammer, K

2008-01-01

We compare two fermionic renormalization group (RG) methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger liquids) and local inhomogeneities. The first one is a poor man's method set-up to resum 'leading-log' divergences of the effective transmission at the Fermi momentum. Generically the resulting equations can be solved analytically. The second approach is based on the functional RG (fRG) method and leads to a set of differential equations which can only for certain set-ups and in limiting cases be solved analytically, while in general it must be integrated numerically. Both methods are claimed to be applicable for inhomogeneities of arbitrary strength and to capture effects of the two-particle interaction, such as interaction dependent exponents, up to leading order. We critically review this for the simplest case of a single impurity. While on first glance the poor man's approach seems to describe the crossover from the 'perfect' to the 'open chain fixed point' we collect evidence that difficulties may arise close to the 'perfect chain fixed point'. Due to a subtle relation between the scaling dimensions of the two fixed points this becomes apparent only in a detailed analysis. In the fRG method the coupling of the different scattering channels is kept which leads to a better description of the underlying physics

Temperature dependence of the electronic structure of semiconductors and insulators

Energy Technology Data Exchange (ETDEWEB)

Poncé, S., E-mail: samuel.pon@gmail.com; Gillet, Y.; Laflamme Janssen, J.; Gonze, X. [European Theoretical Spectroscopy Facility and Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Chemin des étoiles 8, bte L07.03.01, B-1348 Louvain-la-neuve (Belgium); Marini, A. [Consiglio Nazionale delle Ricerche (CNR), Via Salaria Km 29.3, CP 10, 00016 Monterotondo Stazione (Italy); Verstraete, M. [European Theoretical Spectroscopy Facility and Physique des matériaux et nanostructures, Université de Liège, Allée du 6 Août 17, B-4000 Liège (Belgium)

2015-09-14

The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q → Γ, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: α-AlN, β-AlN, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure.

Cosmological constant problem and renormalized vacuum energy density in curved background

Energy Technology Data Exchange (ETDEWEB)

Kohri, Kazunori [Theory Center, IPNS, KEK, Tsukuba 305-0801, Ibaraki (Japan); Matsui, Hiroki, E-mail: kohri@post.kek.jp, E-mail: matshiro@post.kek.jp [The Graduate University of Advanced Studies (Sokendai), Tsukuba 305-0801, Ibaraki (Japan)

2017-06-01

The current vacuum energy density observed as dark energy ρ{sub dark}≅ 2.5×10{sup −47} GeV{sup 4} is unacceptably small compared with any other scales. Therefore, we encounter serious fine-tuning problem and theoretical difficulty to derive the dark energy. However, the theoretically attractive scenario has been proposed and discussed in literature: in terms of the renormalization-group (RG) running of the cosmological constant, the vacuum energy density can be expressed as ρ{sub vacuum}≅ m {sup 2} H {sup 2} where m is the mass of the scalar field and rather dynamical in curved spacetime. However, there has been no rigorous proof to derive this expression and there are some criticisms about the physical interpretation of the RG running cosmological constant. In the present paper, we revisit the RG running effects of the cosmological constant and investigate the renormalized vacuum energy density in curved spacetime. We demonstrate that the vacuum energy density described by ρ{sub vacuum}≅ m {sup 2} H {sup 2} appears as quantum effects of the curved background rather than the running effects of cosmological constant. Comparing to cosmological observational data, we obtain an upper bound on the mass of the scalar fields to be smaller than the Planck mass, m ∼< M {sub Pl}.

A unified effective-field renormalization-group framework approach for the quenched diluted Ising models

Science.gov (United States)

de Albuquerque, Douglas F.; Fittipaldi, I. P.

1994-05-01

A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.

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.

Leading temperature dependence of the conductance in Kondo-correlated quantum dots

Science.gov (United States)

Aligia, A. A.

2018-04-01

Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturbation approach.

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.

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)

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.

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

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.

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

Density dependence of reactor performance with thermal confinement scalings

International Nuclear Information System (INIS)

Stotler, D.P.

1992-03-01

Energy confinement scalings for the thermal component of the plasma published thus far have a different dependence on plasma density and input power than do scalings for the total plasma energy. With such thermal scalings, reactor performance (measured by Q, the ratio of the fusion power to the sum of the ohmic and auxiliary input powers) worsens with increasing density. This dependence is the opposite of that found using scalings based on the total plasma energy, indicating that reactor operation concepts may need to be altered if this density dependence is confirmed in future research

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)

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

Science.gov (United States)

de Sousa, J. Ricardo; Fittipaldi, I. P.

1994-05-01

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

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 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)

Nonequilibrium dynamical renormalization group: Dynamical crossover from weak to infinite randomness in the transverse-field Ising chain

Science.gov (United States)

Heyl, Markus; Vojta, Matthias

2015-09-01

In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems. In particular, the ndRG incorporates time as an additional scale which turns out to be important for the description of the long-time dynamics. It can be applied to both translational-invariant and disordered systems. As a concrete application, we study the real-time dynamics after a quench between two quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. By comparing to numerically exact simulations for large systems, we show that the ndRG is capable of analytically capturing the full crossover from weak to infinite randomness. We analytically study signatures of localization in both real space and Fock space.

Consciousness viewed in the framework of brain phase space dynamics, criticality, and the Renormalization Group

International Nuclear Information System (INIS)

Werner, Gerhard

2013-01-01

The topic of this paper will be addressed in three stages: I will first review currently prominent theoretical conceptualizations of the neurobiology of consciousness and, where appropriate, identify ill-advised and flawed notions in theoretical neuroscience that may impede viewing consciousness as a phenomenon in the physics of brain. In this context, I will also introduce relevant facts that tend not to receive adequate attention in much of the current consciousness discourse. Next, I will review the evidence that accrued in the last decade that identifies the resting brain as being in a state of criticality. In the framework of state phase dynamics of statistical physics, this observational evidence also entails that the resting brain is poised at the brink of a second order phase transition. On this basis, I will in the third stage propose applying the framework of the Renormalization Group to viewing consciousness as a phenomenon in statistical physics. In physics, concepts of phase space transitions and the Renormalization Group are powerful tools for interpreting phenomena involving many scales of length and time in complex systems. The significance of these concepts lies in their accounting for the emergence of different levels of new collective behaviors in complex systems, each level with its distinct macroscopic physics, organization, and laws, as a new pattern of reality. In this framework, I propose to view subjectivity as the symbolic description of the physical brain state of consciousness that emerges as one of the levels of phase transitions of the brain-body-environment system, along the trajectory of Renormalization Group Transformations

Renormalization group improved computation of correlation functions in theories with nontrivial phase diagram

DEFF Research Database (Denmark)

Codello, Alessandro; Tonero, Alberto

2016-01-01

We present a simple and consistent way to compute correlation functions in interacting theories with nontrivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional Z2-scalar theories. The idea is to perform the path integral by weighting...... the momentum modes that contribute to it according to their renormalization group (RG) relevance, i.e. we weight each mode according to the value of the running couplings at that scale. In this way, we are able to encode in a loop computation the information regarding the RG trajectory along which we...

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].

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.)

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

[Development of a New Scale for Gauging Smartphone Dependence].

Science.gov (United States)

Toda, Masahiro; Nishio, Nobuhiro; Takeshita, Tatsuya

2015-01-01

We designed a scale to gauge smartphone dependence and assessed its reliability and validity. A prototype self-rating smartphone-dependence scale was tested on 133 medical students who use smartphones more frequently than other devices to access web pages. Each response was scored on a Likert scale (0, 1, 2, 3), with higher scores indicating greater dependence. To select items for the final scale, exploratory factor analysis was conducted. On the basis of factor analysis results, we designed the Wakayama Smartphone-Dependence Scale (WSDS) comprising 21 items with 3 subscales: immersion in Internet communication; using a smartphone for extended periods of time and neglecting social obligations and other tasks; using a smartphone while doing something else and neglect of etiquette. Our analysis confirmed the validity of the different elements of the WSDS: the reliability coefficient (Cronbach's alpha) values of all subscales and total WSDS were from 0.79 to 0.83 and 0.88, respectively. These findings suggest that the WSDS is a useful tool for rating smartphone dependence.

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.

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...

Mutual information, neural networks and the renormalization group

Science.gov (United States)

Koch-Janusz, Maciej; Ringel, Zohar

2018-06-01

Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains `slow' degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.

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...

A corner transfer matrix renormalization group investigation of the vertex-interacting self-avoiding walk model

Energy Technology Data Exchange (ETDEWEB)

Foster, D P; Pinettes, C [Laboratoire de Physique Theorique et Modelisation (CNRS UMR 8089), Universite de Cergy-Pontoise, 5 Mail Gay-Lussac 95031, Cergy-Pontoise Cedex (France)

2003-10-17

A recently introduced extension of the corner transfer matrix renormalization group method useful for the study of self-avoiding walk-type models is presented in detail and applied to a class of interacting self-avoiding walks due to Bloete and Nienhuis. This model displays two different types of collapse transition depending on model parameters. One is the standard {theta}-point transition. The other is found to give rise to a first-order collapse transition despite being known to be in other respects critical.

Care dependency of hospitalized children: testing the Care Dependency Scale for Paediatrics in a cross-cultural comparison.

Science.gov (United States)

Tork, Hanan; Dassen, Theo; Lohrmann, Christa

2009-02-01

This paper is a report of a study to examine the psychometric properties of the Care Dependency Scale for Paediatrics in Germany and Egypt and to compare the care dependency of school-age children in both countries. Cross-cultural differences in care dependency of older adults have been documented in the literature, but little is known about the differences and similarities with regard to children's care dependency in different cultures. A convenience sample of 258 school-aged children from Germany and Egypt participated in the study in 2005. The reliability of the Care Dependency Scale for Paediatrics was assessed in terms of internal consistency and interrater reliability. Factor analysis (principal component analysis) was employed to verify the construct validity. A Visual Analogue Scale was used to investigate the criterion-related validity. Good internal consistency was detected both for the Arabic and German versions. Factor analysis revealed one factor for both versions. A Pearson's correlation between the Care Dependency Scale for Paediatrics and Visual Analogue Scale was statistically significant for both versions indicating criterion-related validity. Statistically significant differences between the participants were detected regarding the mean sum score on the Care Dependency Scale for Paediatrics. The Care Dependency Scale for Paediatrics is a reliable and valid tool for assessing the care dependency of children and is recommended for assessing the care dependency of children from different ethnic origins. Differences in care dependency between German and Egyptian children were detected, which might be due to cultural differences.

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.).

Grizzly bear habitat selection is scale dependent.

Science.gov (United States)

Ciarniello, Lana M; Boyce, Mark S; Seip, Dale R; Heard, Douglas C

2007-07-01

The purpose of our study is to show how ecologists' interpretation of habitat selection by grizzly bears (Ursus arctos) is altered by the scale of observation and also how management questions would be best addressed using predetermined scales of analysis. Using resource selection functions (RSF) we examined how variation in the spatial extent of availability affected our interpretation of habitat selection by grizzly bears inhabiting mountain and plateau landscapes. We estimated separate models for females and males using three spatial extents: within the study area, within the home range, and within predetermined movement buffers. We employed two methods for evaluating the effects of scale on our RSF designs. First, we chose a priori six candidate models, estimated at each scale, and ranked them using Akaike Information Criteria. Using this method, results changed among scales for males but not for females. For female bears, models that included the full suite of covariates predicted habitat use best at each scale. For male bears that resided in the mountains, models based on forest successional stages ranked highest at the study-wide and home range extents, whereas models containing covariates based on terrain features ranked highest at the buffer extent. For male bears on the plateau, each scale estimated a different highest-ranked model. Second, we examined differences among model coefficients across the three scales for one candidate model. We found that both the magnitude and direction of coefficients were dependent upon the scale examined; results varied between landscapes, scales, and sexes. Greenness, reflecting lush green vegetation, was a strong predictor of the presence of female bears in both landscapes and males that resided in the mountains. Male bears on the plateau were the only animals to select areas that exposed them to a high risk of mortality by humans. Our results show that grizzly bear habitat selection is scale dependent. Further, the

Resummation and renormalization in effective theories of particle physics

CERN Document Server

Jakovac, Antal

2015-01-01

Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to vario...

Scale dependence and small-x behaviour of polarized parton distributions

International Nuclear Information System (INIS)

Ball, R.D.; Forte, S.; Ridolfi, G.

1995-01-01

We discuss perturbative evolution of the polarized structure function g 1 in the (x, Q 2 ) plane, with special regard to the small-x region. We determine g 1 in terms of polarized quark and gluon distributions using coefficient functions to order α s . At small x g 1 then displays substantial scale dependence, which necessarily implies a corresponding scale dependence in the large-x region. This scale dependence has significant consequences for the extraction of the first moment from the experimental data, reducing its value while increasing the error. Conversely, the scale dependence may be used to constrain the size of the polarized gluon distribution. ((orig.))

Scale dependence and small x behaviour of polarized parton distributions

CERN Document Server

Ball, R D; Ridolfi, G; Forte, S; Ridolfi, G

1995-01-01

We discuss perturbative evolution of the polarized structure function g_1 in the (x,Q^2) plane, with special regard to the small-x region. We determine g_1 in terms of polarized quark and gluon distributions using coefficient functions to order alpha_s. At small x g_1 then displays substantial scale dependence, which necessarily implies a corresponding scale dependence in the large-x region. This scale dependence has significant consequences for the extraction of the first moment from the experimental data, reducing its value while increasing the error. Conversely, the scale dependence may be used to constrain the size of the polarized gluon distribution.

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

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.

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.)

Neutrino masses, scale-dependent growth, and redshift-space distortions

Energy Technology Data Exchange (ETDEWEB)

Hernández, Oscar F., E-mail: oscarh@physics.mcgill.ca [Marianopolis College, 4873 Westmount Ave., Westmount, QC H3Y 1X9 (Canada)

2017-06-01

Massive neutrinos leave a unique signature in the large scale clustering of matter. We investigate the wavenumber dependence of the growth factor arising from neutrino masses and use a Fisher analysis to determine the aspects of a galaxy survey needed to measure this scale dependence.

Anomalous scaling in an age-dependent branching model.

Science.gov (United States)

Keller-Schmidt, Stephanie; Tuğrul, Murat; Eguíluz, Víctor M; Hernández-García, Emilio; Klemm, Konstantin

2015-02-01

We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ(-α). Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)(2). This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.

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

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

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

[Creation of a scale for evaluating attitudes of partners toward alcohol dependency].

Science.gov (United States)

Sugawara, Tazuko; Morita, Noriaki; Nakatani, Youji

2013-12-01

The aim of this study was to develop a scale to evaluate characteristics of how alcohol-dependent people perceive the attitudes of their partners toward alcohol dependency. Based on previous research, we created the "Attitudes of partners toward alcohol dependency" scale, from the perspective of the alcohol dependent individual. Using the new scale, 71 alcohol-dependent people (52 men, 19 women) were surveyed after obtaining their consent, and the reliability and validity of the scale were tested. The results identified 3 factors, "indifference", "acceptance" and "hypersensitivity", and factorial validity was verified. Relatively high reliability was obtained on each sub-scale (alpha = .60-.82). Furthermore, correlations were obtained with the alcohol-dependency "Denial and Awareness Scale (for alcohol-dependent people)" and with the 13-item "Usefulness of heterosexual love relations for recovery from alcohol dependency" questionnaire, which includes content on "beneficial" or "obstructive" to recovery, and with the satisfaction and the importance of relations. This demonstrates that the "Attitudes of partners toward alcohol dependency" scale has reliability and criterion-related validity. The scale facilitates evaluation of types of attitudes of partners toward alcohol dependency, and may thus be useful as one tool for investigating the influence of partners in heterosexual love relationships for recovery, and for providing advice.

The renormalization-group flux of the conformally reduced quantum gravity; Der Renormierungsgruppen-Fluss der konform-reduzierten Quantengravitation

Energy Technology Data Exchange (ETDEWEB)

Weyer, Holger

2010-12-17

We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent nonperturbative renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG ow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of Quantum Einstein Gravity (QEG) in the ''conformally reduced'' theory which discards all degrees of freedom contained in the metric except the conformal one. The conformally reduced Einstein-Hilbert approximation has exactly the same qualitative properties as in the full Einstein-Hilbert truncation. In particular it possesses the non-Gaussian fixed point which is necessary for asymptotic safety. Without the extra field dependence the resulting RG flow is that of a simple {phi}{sup 4}-theory. We employ the Local Potential Approximation for the conformal factor to generalize the RG flow on an infinite dimensional theory space. Again we find a Gaussian as well as a non-Gaussian fixed point which provides further evidence for the viability of the asymptotic safety scenario. The analog of the invariant cubic in the curvature which spoils perturbative renormalizability is seen to be unproblematic for the asymptotic safety of the conformally reduced theory. The scaling fields and dimensions of both fixed points are obtained explicitly and possible implications for the predictivity of the theory are discussed. Since the RG flow depends on the topology of the

Slowest kinetic modes revealed by metabasin renormalization

Science.gov (United States)

Okushima, Teruaki; Niiyama, Tomoaki; Ikeda, Kensuke S.; Shimizu, Yasushi

2018-02-01

Understanding the slowest relaxations of complex systems, such as relaxation of glass-forming materials, diffusion in nanoclusters, and folding of biomolecules, is important for physics, chemistry, and biology. For a kinetic system, the relaxation modes are determined by diagonalizing its transition rate matrix. However, for realistic systems of interest, numerical diagonalization, as well as extracting physical understanding from the diagonalization results, is difficult due to the high dimensionality. Here, we develop an alternative and generally applicable method of extracting the long-time scale relaxation dynamics by combining the metabasin analysis of Okushima et al. [Phys. Rev. E 80, 036112 (2009), 10.1103/PhysRevE.80.036112] and a Jacobi method. We test the method on an illustrative model of a four-funnel model, for which we obtain a renormalized kinematic equation of much lower dimension sufficient for determining slow relaxation modes precisely. The method is successfully applied to the vacancy transport problem in ionic nanoparticles [Niiyama et al., Chem. Phys. Lett. 654, 52 (2016), 10.1016/j.cplett.2016.04.088], allowing a clear physical interpretation that the final relaxation consists of two successive, characteristic processes.

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

Critical asymmetry in renormalization group theory for fluids.

Science.gov (United States)

Zhao, Wei; Wu, Liang; Wang, Long; Li, Liyan; Cai, Jun

2013-06-21

The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.

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

Comparative interpretations of renormalization inversion technique for reconstructing unknown emissions from measured atmospheric concentrations

Science.gov (United States)

Singh, Sarvesh Kumar; Kumar, Pramod; Rani, Raj; Turbelin, Grégory

2017-04-01

The study highlights a theoretical comparison and various interpretations of a recent inversion technique, called renormalization, developed for the reconstruction of unknown tracer emissions from their measured concentrations. The comparative interpretations are presented in relation to the other inversion techniques based on principle of regularization, Bayesian, minimum norm, maximum entropy on mean, and model resolution optimization. It is shown that the renormalization technique can be interpreted in a similar manner to other techniques, with a practical choice of a priori information and error statistics, while eliminating the need of additional constraints. The study shows that the proposed weight matrix and weighted Gram matrix offer a suitable deterministic choice to the background error and measurement covariance matrices, respectively, in the absence of statistical knowledge about background and measurement errors. The technique is advantageous since it (i) utilizes weights representing a priori information apparent to the monitoring network, (ii) avoids dependence on background source estimates, (iii) improves on alternative choices for the error statistics, (iv) overcomes the colocalization problem in a natural manner, and (v) provides an optimally resolved source reconstruction. A comparative illustration of source retrieval is made by using the real measurements from a continuous point release conducted in Fusion Field Trials, Dugway Proving Ground, Utah.

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

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.

Minimum scaling laws in tokamaks

International Nuclear Information System (INIS)

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

1986-10-01

Scaling laws governing anomalous electron transport in tokamaks with ohmic and/or auxiliary heating are derived using renormalized Vlasov-Ampere equations for low frequency electromagnetic microturbulence. It is also shown that for pure auxiliary heating (or when auxiliary heating power far exceeds the ohmic power), the energy confinement time scales as tau/sub E/ ∼ P/sub inj//sup -1/3/, where P/sub inj/ is the injected power

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.

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.

Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC

Energy Technology Data Exchange (ETDEWEB)

Wang, Sheng-Quan; Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin

2016-09-09

We present improved perturbative QCD (pQCD) predictions for Higgs boson hadroproduction at the LHC by applying the principle of maximum conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale μ r of the QCD coupling α s ( μ r ) is the Higgs mass and then to vary this choice over the range 1 / 2 m H < μ r < 2 m H in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the nonconformal β terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where a pQCD series has large higher-order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this ad hoc choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading-order RG resummed pQCD predictions for Higgs boson hadroproduction which are renormalization-scheme independent and have minimal sensitivity to the choice of the initial renormalization scale. Taking m H = 125 GeV , the PMC predictions for the p p → H X Higgs inclusive hadroproduction cross sections for various LHC center-of-mass energies are σ Incl | 7 TeV = 21.2 1 + 1.36 - 1.32 pb , σ Incl | 8 TeV = 27.3 7 + 1.65 - 1.59 pb , and σ Incl | 13 TeV = 65.7 2 + 3.46 - 3.0 pb . We also predict the fiducial cross section σ fid ( p p → H → γ γ ) : σ fid | 7 TeV = 30.1 + 2.3 - 2.2 fb , σ fid | 8 TeV = 38.3 + 2.9 - 2.8 fb , and σ fid | 13 TeV = 85.8 + 5.7 - 5.3 fb . The error limits in these predictions include the small residual high

Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory

International Nuclear Information System (INIS)

Chen, G.-H.; Wu, Y.-S.

2002-01-01

A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents ν m and β k , whose values are determined to be 1/4 and 1/2, respectively, at mean-field level

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.)

Validity and factor structure of the bodybuilding dependence scale.

Science.gov (United States)

Smith, D; Hale, B

2004-04-01

To investigate the factor structure, validity, and reliability of the bodybuilding dependence scale and to investigate differences in bodybuilding dependence between men and women and competitive and non-competitive bodybuilders. Seventy two male competitive bodybuilders, 63 female competitive bodybuilders, 87 male non-competitive bodybuilders, and 63 non-competitive female bodybuilders completed the bodybuilding dependence scale (BDS), the exercise dependence questionnaire (EDQ), and the muscle dysmorphia inventory (MDI). Confirmatory factor analysis of the BDS supported a three factor model of bodybuilding dependence, consisting of social dependence, training dependence, and mastery dependence (Q = 3.16, CFI = 0.98, SRMR = 0.04). Internal reliability of all three subscales was high (Cronbach's alpha = 0.92, 0.92, and 0.93 respectively). Significant (pbodybuilders scored significantly (pbodybuilders. However, there were no significant sex differences on any of the BDS subscales (p>0.05). The three factor BDS appears to be a reliable and valid measure of bodybuilding dependence. Symptoms of bodybuilding dependence are more prevalent in competitive bodybuilders than non-competitive ones, but there are no significant sex differences in bodybuilding dependence.

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

Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media: SCALE-DEPENDENT UQ

Energy Technology Data Exchange (ETDEWEB)

Tartakovsky, A. M. [Computational Mathematics Group, Pacific Northwest National Laboratory, Richland WA USA; Panzeri, M. [Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milano Italy; Tartakovsky, G. D. [Hydrology Group, Pacific Northwest National Laboratory, Richland WA USA; Guadagnini, A. [Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milano Italy

2017-11-01

Equations governing flow and transport in heterogeneous porous media are scale-dependent. We demonstrate that it is possible to identify a support scale $\\eta^*$, such that the typically employed approximate formulations of Moment Equations (ME) yield accurate (statistical) moments of a target environmental state variable. Under these circumstances, the ME approach can be used as an alternative to the Monte Carlo (MC) method for Uncertainty Quantification in diverse fields of Earth and environmental sciences. MEs are directly satisfied by the leading moments of the quantities of interest and are defined on the same support scale as the governing stochastic partial differential equations (PDEs). Computable approximations of the otherwise exact MEs can be obtained through perturbation expansion of moments of the state variables in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for the standard deviation smaller than one. We demonstrate our approach in the context of steady-state groundwater flow in a porous medium with a spatially random hydraulic conductivity.

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

Semicontinuity of 4d N=2 spectrum under renormalization group flow

International Nuclear Information System (INIS)

Xie, Dan; Yau, Shing-Tung

2016-01-01

We study renormalization group flow of four dimensional N=2 SCFTs defined by isolated hypersurface three-fold singularities. We define the spectrum of N=2 theory as the set of scaling dimensions of the parameters on the Coulomb branch, which include Coulomb branch moduli, mass parameters and coupling constants. We prove that the spectrum of those theories is semicontinous under the RG flow on the Coulomb branch using the mathematical result about the singularity spectra under deformation. The semicontinuity behavior of N=2 spectrum implies a theorem under relevant and Coulomb branch moduli deformation, the absence of dangerous irrelevant deformations and can be taken as the necessary condition for the ending point of a RG flow. This behavior is also true for (c,c) ring deformation of two dimensional Landau-Ginzburg model with (2,2) supersymmetry.

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.

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.)

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

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

A reliability and utility study of the Care Dependency Scale

NARCIS (Netherlands)

Dijkstra, A.; Buist, G.; Moorer, P.; Dassen, T.

2000-01-01

The purpose of this study was to examine the reliability and utility of the Care Dependency Scale (CDS). This 15-item scale has been developed recently for assessing the care dependency of demented or menially handicapped inpatients. Data for this study were collected from 153 demented and 139

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)

Comparison of renormalization group schemes for sine-Gordon-type models

International Nuclear Information System (INIS)

Nandori, I.; Nagy, S.; Sailer, K.; Trombettoni, A.

2009-01-01

The scheme dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoretic models discussing the applicability of various functional RG methods in detail. It was shown that scheme-independent determination of such physical parameters is possible as the critical frequency (temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition takes place in the sine-Gordon and the layered sine-Gordon models, and the critical ratio characterizing the Ising-type phase transition of the massive sine-Gordon model. For the latter case, the Maxwell construction represents a strong constraint on the RG flow, which results in a scheme-independent infrared value for the critical ratio. For the massive sine-Gordon model also the shrinking of the domain of the phase with spontaneously broken periodicity is shown to take place due to the quantum fluctuations.

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.

RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations

Science.gov (United States)

Bi, Yujiang; Cai, Hao; Chen, Ying; Gong, Ming; Liu, Keh-Fei; Liu, Zhaofeng; Yang, Yi-Bo; χ QCD Collaboration

2018-05-01

Renormalization constants (RCs) of overlap quark bilinear operators on 2 +1 -flavor domain wall fermion configurations are calculated by using the RI/MOM and RI/SMOM schemes. The scale independent RC for the axial vector current is computed by using a Ward identity. Then the RCs for the quark field and the vector, tensor, scalar, and pseudoscalar operators are calculated in both the RI/MOM and RI/SMOM schemes. The RCs are converted to the MS ¯ scheme and we compare the numerical results from using the two intermediate schemes. The lattice size is 4 83×96 and the inverse spacing 1 /a =1.730 (4 ) GeV .

Alternating chain with Hubbard-type interactions: renormalization group analysis

International Nuclear Information System (INIS)

Buzatu, F. D.; Jackeli, G.

1998-01-01

A large amount of work has been devoted to the study of alternating chains for a better understanding of the high-T c superconductivity mechanism. The same phenomenon renewed the interest in the Hubbard model and in its one-dimensional extensions. In this work we investigate, using the Renormalization Group (RG) method, the effect of the Hubbard-type interactions on the ground-state properties of a chain with alternating on-site atomic energies. The one-particle Hamiltonian in the tight binding approximation corresponding to an alternating chain with two nonequivalent sites per unit cell can be diagonalized by a canonical transformation; one gets a two band model. The Hubbard-type interactions give rise to both intra- and inter-band couplings; however, if the gap between the two bands is sufficiently large and the system is more than half-filled, as for the CuO 3 chain occurring in high-T c superconductors, the last ones can be neglected in describing the low energy physics. We restrict our considerations to the Hubbard-type interactions (upper band) in the particular case of alternating on-site energies and equal hopping amplitudes. The standard RG analysis (second order) is done in terms of the g-constants describing the elementary processes of forward, backward and Umklapp scatterings: their expressions are obtained by evaluating the Hubbard-type interactions (upper band) at the Fermi points. Using the scaling to the exact soluble models Tomonaga-Luttinger and Luther-Emery, we can predict the low energy physics of our system. The ground-state phase diagrams in terms of the model parameters and at arbitrary band filling are determined, where four types of instabilities have been considered: Charge Density Waves (CDW), Spin Density Waves (SDW), Singlet Superconductivity (SS) and Triplet Superconductivity (TS). The 3/4-filled case in terms of some renormalized Hubbard constants is presented. The relevance of our analysis to the case of the undistorted 3/4-filled Cu

The generalized scheme-independent Crewther relation in QCD

Science.gov (United States)

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; Brodsky, Stanley J.

2017-07-01

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton-nucleon scattering times the Adler function, defined from the cross section for electron-positron annihilation into hadrons, has no pQCD radiative corrections. The ;Generalized Crewther Relation; relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (Dns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (CBjp) at leading twist. A scheme-dependent ΔCSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both Dns and the inverse coefficient CBjp-1 have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, αˆd (Q) =∑i≥1 αˆg1 i (Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Similar