Non-perturbative renormalization flow in quantum field theory and statistical physics

By J. Berges, N. Tetradis, C. Wetterich. 2000

975 citations recorded by the source corpus.

Abstract We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O ( N )-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz–Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid–gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high-temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular, we explore chiral symmetry breaking and the high-temperature or high-density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/833a96c8a7a8db23ccbec6d55c52ce84d43039db

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Citations in the corpus

Universality classes in nonequilibrium lattice systems (2002, methodology): “The static critical exponents have been determined by e=4−d expansions up to five-loop order sGorishny et al., 1984d, by exact RG methods ssee Berges et al., 2002 and references thereind, by simulations sHasenbuch, 2001d and by series expansions in three dimensions ssee Guida and Zinn-Justin, 1998,…”
Cosmology of the Lifshitz universe (2009, background): “These models can be studied with renormalization group (RG) techniques [54, 57, 58, 59, 60].”
The nonperturbative functional renormalization group and its applications (2020, background): “All fluctuations are then frozen and Γkin [φ] = S [φ] [60] as in Landau’s mean-field theory of phase transitions.”
The QCD running coupling (2016, neutral): “[345].”
The Asymptotic Safety Scenario in Quantum Gravity (2006, methodology): “Both aspects have been tested in Yang–Mills theories, we refer to [229, 29] for a review and further literature.”
QCD at finite temperature and chemical potential from Dyson–Schwinger equations (2018, positive): “Closely related to the formalism of Dyson-Schwinger equations is the one for the functional renormalization group (FRG), see [194, 195] and the reviews [196–199].”
Functional renormalization group approach to correlated fermion systems (2011, methodology): “The functional ΓΛR and its analog for bosonic fields is known as effective average action in the literature (Berges et al., 2002).”