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.

MASSIVE AXIAL GAUGE IN THE EXACT RENORMALIZATION GROUP APPROACH

2001 ◽  
Vol 16 (11) ◽  
pp. 2101-2104 ◽  
Author(s):  
P. PANZA ◽  
R. SOLDATI
Keyword(s):  
Renormalization Group ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Massless Limit ◽  
Group Approach ◽  
Gauge Invariant ◽  
Axial Gauge ◽  
Renormalization Group Approach ◽  
Exact Renormalization Group

The Exact Renormalization Group (ERG) approach to massive gauge theories in the axial gauge is studied and the smoothness of the massless limit is analysed for a formally gauge invariant quantity such as the Euclidean Wilson loop.

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.

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