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The nonperturbative functional renormalization group and its applications

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 May 2021Embargo end date: 01 Jan 2020 France, Denmark Publisher:Elsevier BVJournal:Physics Reports, volume 910, pages 1-114 (issn: 0370-1573, Copyright policy )Funded by:DFG | unidentified, UKRI | Cadmium Replacement Using...
Authors: W. Metzner; Matthieu Tissier; Astrid Eichhorn; Astrid Eichhorn; Léonie Canet; Nicolás Wschebor; Jan M. Pawlowski; +1 Authors

doi: 10.1016/j.physrep.2021.01.001 , 10.48550/arxiv.2006.04853

arXiv: http://arxiv.org/abs/2006.04853

The nonperturbative functional renormalization group and its applications

Abstract

The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.

v3) Review article, 93 pages + bibliography, 35 figures

Countries
France, Denmark
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Keywords

High Energy Physics - Theory, [PHYS.PHYS.PHYS-GEN-PH] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), 530, General Relativity and Quantum Cosmology, High Energy Physics - Phenomenology (hep-ph), ultraviolet, Field theory, Condensed Matter - Statistical Mechanics, Functional methods, [PHYS.GRQC] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], Statistical Mechanics (cond-mat.stat-mech), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], approximation: nonperturbative, free energy, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], [PHYS.HPHE] Physics [physics]/High Energy Physics - Phenomenology [hep-ph], High Energy Physics - Phenomenology, effective action, High Energy Physics - Theory (hep-th), quantum gravity, [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], flow, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], statistical mechanics, renormalization group, Renormalization group, statistical

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 411
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 0.1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 1%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
411
Top 0.1%
Top 1%
Top 0.01%
Green
bronze
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