In theoretical physics, functional renormalization group (FRG) is an implementation of the renormalization group (RG) concept which is used in quantum and statistical field theory, especially when dealing with strongly interacting systems. The method combines functional methods of quantum field theory with the intuitive renormalization group idea of Kenneth G. Wilson. This technique allows to interpolate smoothly between the known microscopic laws and the complicated macroscopic phenomena in physical systems. In this sense, it bridges the transition from simplicity of microphysics to complexity of macrophysics. Figuratively speaking, FRG acts as a microscope with a variable resolution. One starts with a high-resolution picture of the known microphysical laws and subsequently decreases the resolution to obtain a coarse-grained picture of macroscopic collective phenomena. The method is nonperturbative, meaning that it does not rely on an expansion in a small coupling constant. Mathematically, FRG is based on an exact functional differential equation for a scale-dependent effective action.
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Its key ingredient is a nontrivial fixed point of the theory's renormalizationgroup flow which controls the behavior of the coupling constants in the...
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particle physics. The development of the theoretical method of functionalrenormalization by Wetterich has found applications in many areas of physics,...
Wilson further pioneered the power of renormalization concepts by developing the formalism of renormalizationgroup (RG) theory, to investigate critical...
Costello's monograph Renormalization and Effective Field Theory provides a rigorous formulation of perturbative renormalization that combines both the...
Mathematical Society) 2003 with Feldman, Knörrer: Fermionic functional integrals and the renormalizationgroup, AMS 2002 with D. Gieseker, Knörrer: Geometry of algebraic...
on the momentum (or length) scale is the central idea behind the renormalizationgroup. Landau poles appear in theories that are not asymptotically free...
of some computations: for example Ward identities connect different renormalization constants. The first gauge theory quantized was quantum electrodynamics...
particular, the renormalization theory for interacting fermionic systems and the fluctuation relation for the large deviation functional of entropy production...
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the...
renormalization of the underlying Yang–Mills theory fields and couplings does not prevent the Wilson loops from requiring additional renormalization corrections...
he collaborated with Antti Kupiainen on the application of the renormalizationgroup method in the rigorous mathematical treatment of various model systems...
with it many techniques, such as the path integral formulation and renormalization. If the system involves polymers, it is also known as polymer field...
model. The theoretical treatment in generic dimensions requires the renormalizationgroup approach or the conformal bootstrap techniques. Phase transitions...
Presently, effective field theories are discussed in the context of the renormalizationgroup (RG) where the process of integrating out short distance degrees...
of normed vector space was in the air, and in the 1920s Banach created functional analysis. In mathematics, a metric space is a set where a notion of distance...
quantization so far, for reasons related to renormalization. Another class of gauge theories with a non-Abelian gauge group, beginning with Yang–Mills theory,...
and operators, numerical linear algebra can also be viewed as a type of functional analysis which has a particular emphasis on practical algorithms.: ix ...
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