“Environmentally Friendly” Renormalization

O’Connor, Denjoe; Stephens, Christopher R.

doi:10.1142/s0217751x94001151

Cited by 45 publications

(76 citation statements)

References 40 publications

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“…For example, we are used to fixing the ambiguities of renormalization theory by demanding certain Green functions to take on given values under certain conditions (conditions which should resemble the physical situation of interest as much as possible, as discussed by O'Connor and Stephens [55]). If the Green functions themselves are to be regarded as fluctuating, then the same ought to hold for the renormalized coupling constants defined from them, and to the renormalization group (RG) equations describing their scale dependence.…”

Section: Discussionmentioning

confidence: 99%

Stochastic dynamics of correlations in quantum field theory: From the Schwinger-Dyson to Boltzmann-Langevin equation

Calzetta

1999

Phys. Rev. D

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The aim of this paper is two-fold: in probing the statistical mechanical properties of interacting quantum fields, and in providing a field theoretical justification for a stochastic source term in the Boltzmann equation. We start with the formulation of quantum field theory in terms of the Schwinger -Dyson equations for the correlation functions, which we describe by a closed-time-path master (n = ∞P I) effective action. When the hierarchy is truncated, one obtains the ordinary closed-system of correlation functions up to a certain order, and from the nPI effective action, a set of time-reversal invariant equations of motion. But when the effect of the higher order correlation functions is included (through e.g., causal factorization-molecular chaos -conditions, which we call 'slaving'), in the form of a correlation noise, the dynamics of the lower order correlations shows dissipative features, as familiar in the field-theory version of Boltzmann equation. We show that fluctuation-dissipation relations exist for such effectively open systems, and use them to show that such a stochastic term, which explicitly introduces quantum fluctuations on the lower order correlation functions, necessarily accompanies the dissipative term, thus leading to a Boltzmann-Langevin equation which depicts both the dissipative and stochastic dynamics of correlation functions in quantum field theory.

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Section: Discussionmentioning

confidence: 99%

Stochastic dynamics of correlations in quantum field theory: From the Schwinger-Dyson to Boltzmann-Langevin equation

Calzetta

1999

Phys. Rev. D

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“…3 In this sense our formulation is a sort of the "environmentally friendly renormalization group", which has been proposed by O'Connor and Stephens [19]. 4 For the NJL model this scheme is nothing but the large N leading approximation.…”

Section: The Rg Equations With the Collective Fieldmentioning

confidence: 99%

Analysis of the Wilsonian effective potentials in dynamical chiral symmetry breaking

et al. 2000

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The non-perturbative renormalization group equation for the Wilsonian effective potential is given in a certain simple approximation scheme in order to study chiral symmetry breaking phenomena dynamically induced by strong gauge interactions. The evolving effective potential is found to be non-analytic in infrared, which indicates spontaneous generation of the fermion mass. It is also shown that the renormalization group equation gives the identical effective fermion mass with that obtained by solving the SchwingerDyson equation in the (improved) ladder approximation. Moreover introduction of the collective field corresponding to the fermion composite into the theory space is found to offer an efficient method to evaluate the order parameters; the dynamical mass and the chiral condensate. The relation between the renormalization group equation incorporating the collective field and the Schwinger-Dyson equation is also clarified.

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“…The studies of the fluctuating character of these field theoretic Green functions also suggest new avenues in the development of RG theory. For example, we are used to fixing the ambiguities of renormalization theory by demanding certain Green functions to take on given values under certain conditions (conditions which should resemble the physical situation of interest as much as possible, as stressed by O'Connor and Stephens [109]). If the Green functions themselves are to be regarded as fluctuating, then the same ought to hold for the renormalized coupling constants defined from them, and for the renormalization group (RG) equations describing their scale dependence.…”

Section: Stochastic Rg Equationsmentioning

confidence: 99%

Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology

Calzetta

Mazzitelli

2001

Physics Reports

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In this report we introduce the basic techniques (of the closed-time-path coarse-grained effective action) and ideas (scaling, coarse-graining and backreaction) behind the treatment of quantum processes in dynamical background spacetimes and fields. We show how they are useful for the construction of renormalization group (RG) theories for studying these nonequilibrium processes and discuss the underlying issues. Examples are drawn from quantum field processes in an inflationary universe, semiclassical cosmology and stochastic gravity. In Part I we begin by establishing a relation between scaling and inflation, and show how eternal inflation (where the scale factor of the universe grows exponentially) can be treated as static critical phenomena, while a 'slow-roll' or power-law inflation can be treated as dynamical critical phenomena. In Part II we introduce the key concepts in open systems and discuss the relation of coarse-graining and backreaction. We recount how the (in-out, or Schwinger-DeWitt) coarse-grained effective action (CGEA) devised by Hu and Zhang can be used to treat some aspects of the effects of the environment on the system. This is illustrated by the stochastic inflation model where quantum fluctuations appearing as noise backreact on the inflaton field. We show how RG techniques can be usefully applied to obtain the running of coupling constants in the inflaton field, followed by a discussion of the cosmological and theoretical implications. In Part III we present the Closed-Time-Path (CTP, in-in, or Schwinger-Keldysh) CGEA introduced by Hu and Sinha. We show how to calculate perturbatively the CTP CGEA for the λΦ 4 model. We mention how it is useful for calculating the backreaction of environmental fields on the system field (e.g. light on heavy, fast on slow) or one sector of a field on another (e.g. high momentum modes on low, inhomogeneous modes on homogeneous), and problems in other areas of physics where this method can be usefully applied. This is followed by an introduction to the influence functional in the (Feynman-Vernon) formulation of quantum open systems, illustrated by the quantum Brownian motion models. We show its relation to the CTP CGEA, and indicate how to identify the noise and dissipation kernels therein. We derive the master and Langevin equations for interacting quantum fields, represented in the works of Lombardo and Mazzitelli and indicate how they can be applied to the problem of coarse-graining, decoherence and structure formation in de Sitter universe. We perform a nonperturbative evaluation of the CTP CGEA and show how to derive the renormalization group equations under an adiabatic approximation adopted for the modes by Dalvit and Mazzitelli. We assert that this approximation is incomplete as the effect of noise is suppressed. We then discuss why noise is expected in the RG equations for nonequilibrium processes. In Part IV, following *

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“Environmentally Friendly” Renormalization

Cited by 45 publications

References 40 publications

Stochastic dynamics of correlations in quantum field theory: From the Schwinger-Dyson to Boltzmann-Langevin equation

Stochastic dynamics of correlations in quantum field theory: From the Schwinger-Dyson to Boltzmann-Langevin equation

Analysis of the Wilsonian effective potentials in dynamical chiral symmetry breaking

Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology

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