Gauge symmetry and the functional renormalization group

2017 ◽  
Vol 32 (35) ◽  
pp. 1747011 ◽  
Author(s):  
Katsumi Itoh
Keyword(s):  
Renormalization Group ◽  
Gauge Symmetry ◽  
Exponential Type ◽  
Flow Equation ◽  
Point Function ◽  
Functional Renormalization Group ◽  
Analytical Expression

In the functional renormalization group (FRG), the introduction of a momentum cutoff often breaks symmetry present in a theory. The most important example is the gauge symmetry. However a symmetry survives in the presence of a cutoff in a modified form. We apply our understanding to QED as the simplest case. A modified version of the Ward–Takahashi identity is solved partially to constrain the Wilson action. Furthermore, we study the flow equation for the photon 2-point function and find its analytical expression for the regulator function of the exponential type.

scholarly journals Multi-regulator functional renormalization group for many-fermion systems

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740027
Author(s):  
Yuya Tanizaki ◽  
Tetsuo Hatsuda
Keyword(s):  
Renormalization Group ◽  
Collective Excitations ◽  
Einstein Condensation ◽  
Point Function ◽  
Functional Renormalization Group ◽  
Fermionic System ◽  
Bose Einstein Condensation ◽  
Fermion Systems ◽  
Two Component ◽  
Bose Einstein

We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.

scholarly journals Alternative flow equation for the functional renormalization group

2019 ◽  
Vol 100 (10) ◽  
Author(s):  
Elizabeth Alexander ◽  
Peter Millington ◽  
Jordan Nursey ◽  
Paul M. Saffin
Keyword(s):  
Renormalization Group ◽  
Flow Equation ◽  
Functional Renormalization Group

scholarly journals Effective action from the functional renormalization group

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Nobuyoshi Ohta ◽  
Lesław Rachwał
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Dirac Fermions ◽  
Charged Scalar ◽  
Functional Renormalization Group ◽  
Scale Down ◽  
Nonlocal Terms

AbstractWe study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the “exact” or “functional” renormalization group equation to derive the effective action $$\Gamma _0$$ Γ 0 by integrating the flow equation from the ultraviolet scale down to $$k=0$$ k = 0 . The resulting effective action consists of local terms and nonlocal terms with unique coefficients.

scholarly journals Erratum: Alternative flow equation for the functional renormalization group [Phys. Rev. D 100 , 101702(R) (2019)]

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Elizabeth Alexander ◽  
Peter Millington ◽  
Jordan Nursey ◽  
Paul M. Saffin
Keyword(s):  
Renormalization Group ◽  
Flow Equation ◽  
Functional Renormalization Group
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