scholarly journals GAUGE CONSISTENT WILSON RENORMALIZATION GROUP I: THE ABELIAN CASE

2000 ◽  
Vol 15 (14) ◽  
pp. 2121-2151 ◽  
Author(s):  
M. SIMIONATO
Keyword(s):  
Renormalization Group ◽  
Gauge Symmetry ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Group I ◽  
Abelian Case ◽  
Exact Renormalization Group ◽  
Wilson Renormalization Group

A version of the Exact Renormalization Group Equation consistent with gauge symmetry is presented. A discussion of its regularization and renormalization is given. The relation with the Callan–Symanzik equation is clarified.

scholarly journals LOOP VARIABLES IN STRING THEORY

2003 ◽  
Vol 18 (05) ◽  
pp. 767-809 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

scholarly journals SOLUTIONS OF THE POLCHINSKI ERG EQUATION IN THE O(N) SCALAR MODEL

2002 ◽  
Vol 17 (32) ◽  
pp. 4871-4902 ◽  
Author(s):  
YU. A. KUBYSHIN ◽  
R. NEVES ◽  
R. POTTING
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Scalar Model ◽  
Regular Solutions ◽  
Exact Renormalization Group

Solutions of the Polchinski exact renormalization group equation in the scalar O(N) theory are studied. Families of regular solutions are found and their relation with fixed points of the theory is established. Special attention is devoted to the limit N = ∞, where many properties can be analyzed analytically.

scholarly journals THE EXACT RENORMALIZATION GROUP IN ASTROPHYSICS

2001 ◽  
Vol 16 (11) ◽  
pp. 2041-2046 ◽  
Author(s):  
JOSÉ GAITE
Keyword(s):  
Renormalization Group ◽  
Probability Distribution ◽  
Time Evolution ◽  
Planck Equation ◽  
Coarse Graining ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Change Of Scale ◽  
Exact Renormalization Group ◽  
Fokker Planck

The coarse-graining operation in hydrodynamics is equivalent to a change of scale which can be formalized as a renormalization group transformation. In particular, its application to the probability distribution of a self-gravitating fluid yields an "exact renormalization group equation" of Fokker-Planck type. Since the time evolution of that distribution can also be described by a Fokker-Planck equation, we propose a connection between both equations, that is, a connection between scale and time evolution. We finally remark on the essentially non-perturbative nature of astrophysical problems, which suggests that the exact renormalization group is the adequate tool for them.

scholarly journals Exact Renormalization Group Approach in Scalar and Fermionic Theories

1998 ◽  
Vol 12 (12n13) ◽  
pp. 1321-1341 ◽  
Author(s):  
Yu. Kubyshin
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Derivative Expansion ◽  
Group Approach ◽  
Renormalization Group Approach ◽  
Exact Renormalization Group

The Polchinski version of the exact renormalization group equation is discussed and its applications in scalar and fermionic theories are reviewed. Relation between this approach and the standard renormalization group is studied, in particular the relation between the derivative expansion and the perturbation theory expansion is worked out in some detail.

scholarly journals SCHEME INDEPENDENCE AS AN INHERENT REDUNDANCY IN QUANTUM FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2071-2074 ◽  
Author(s):  
JOSÉ I. LATORRE ◽  
TIM R. MORRIS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Quantum Field ◽  
Renormalization Group Equations ◽  
Field Transformation ◽  
Exact Renormalization Group ◽  
Infinite Set

The path integral formulation of Quantum Field Theory implies an infinite set of local, Schwinger-Dyson-like relation. Exact renormalization group equations can be cast as a particular instance of these relations. Furthermore, exact scheme independence is turned into a vector field transformation of the kernel of the exact renormalization group equation under field redefinitions.

scholarly journals Renormalization group and diffusion equation

2020 ◽  
Author(s):  
Masami Matsumoto ◽  
Gota Tanaka ◽  
Asato Tsuchiya
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Diffusion Equation ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Initial Time ◽  
Group Equation ◽  
Cutoff Function ◽  
Exact Renormalization Group ◽  
And Diffusion

Abstract We study relationship between renormalization group and diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed action. As a generalization of the result obtained by Sonoda and Suzuki, we find that the correlation functions of diffused fields with respect to the bare action agree with those of bare fields with respect to the effective action, where the diffused field obeys a generalized diffusion equation determined by the cutoff function and the seed action and agrees with the bare field at the initial time.

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