Introduction to the Functional Renormalization Group

Kopietz, Peter; Bartosch, Lorenz; Schütz, Florian

doi:10.1007/978-3-642-05094-7

Cited by 425 publications

(756 citation statements)

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“…Specific examples will be discussed below. For reviews of the functional RG see [33][34][35][36][37]. From the full effective action in the long-wavelength limit…”

Section: Microscopic Model and The Functional Renormalization Groupmentioning

confidence: 99%

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Scherer

Floerchinger

Gies

2011

Phil. Trans. R. Soc. A.

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We review the functional renormalization group (RG) approach to the Bardeen-CooperSchrieffer to Bose-Einstein condensation (BCS-BEC) crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature, which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

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“…Specific examples will be discussed below. For reviews of the functional RG see [33][34][35][36][37]. From the full effective action in the long-wavelength limit…”

Section: Microscopic Model and The Functional Renormalization Groupmentioning

confidence: 99%

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Scherer

Floerchinger

Gies

2011

Phil. Trans. R. Soc. A.

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“…In order to incorporate fluctuations in a self-consistent manner, the functional renormalization group (FRG) method is used ( [9] and references therein). The effective action, Γ k , at a renormalization scale k, interpolates in this framework between the microscopic action, S = Γ k=Λ , at a cutoff scale Λ and the full effective action, Γ eff = Γ k=0 , with all fluctuations integrated out.…”

Section: Adding Fluctuationsmentioning

confidence: 99%

Dense nucleonic matter and the renormalization group

Drews

Hell

Klein

et al. 2014

EPJ Web of Conferences

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Abstract. Fluctuations are included in a chiral nucleon-meson model within the framework of the functional renormalization group. The model, with parameters fitted to reproduce the nuclear liquid-gas phase transition, is used to study the phase diagram of QCD. We find good agreement with results from chiral effective field theory. Moreover, the results show a separation of the chemical freeze-out line and chiral symmetry restoration at large baryon chemical potentials.

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“…The scale dependence of the averaged action is characterized by the flow equation [18][19][20] in momentum representation,…”

Section: Application Of Functional Renormalization To Thementioning

confidence: 99%

“…In order to complete the set of flow equations, we need equations for the evolution of Z Sk and Z P k [20]. To the one-loop level they read…”

Section: Application Of Functional Renormalization To Thementioning

confidence: 99%

Functional renormalization for chiral andUA(1)symmetries at finite temperature

Jiang

Zhuang

2012

Phys. Rev. D

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We investigated the chiral symmetry and UA(1) anomaly at finite temperature by applying the functional renormalization group to the SU (3) linear sigma model. Expanding the local potential around the classical fields, we derived the flow equations for the renormalization parameters. In chiral limit, the flow equation for the chiral condensate is decoupled from the others and can be analytically solved. The Goldstone theorem is guaranteed in vacuum and at finite temperature, and the two phase transitions for the chiral and UA(1) symmetry restoration happen at the same critical temperature. In general case with explicit chiral symmetry breaking, the two symmetries are partially and slowly restored, and the scalar and pseudoscalar meson masses are controlled by the restoration in the limit of high temperature.

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Introduction to the Functional Renormalization Group

Cited by 425 publications

References 0 publications

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Dense nucleonic matter and the renormalization group

Functional renormalization for chiral andUA(1)symmetries at finite temperature

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