Renormalization group and renormalization theory in p-adic and adelic scalar models

1991 ◽  
pp. 143-164 ◽  
Author(s):  
M. Missarov
Keyword(s):  
Renormalization Group ◽  
Renormalization Theory

Introduction to renormalization theory and renormalization group (RG)

2021 ◽  
pp. 185-219
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Short Distance ◽  
Large Scale ◽  
Relativistic Quantum ◽  
Power Counting ◽  
Fine Tuning ◽  
Quantum Field ◽  
Renormalizable Theory ◽  
Renormalization Theory

A straightforward construction of a local, relativistic quantum field theory (QFT) leads to ultraviolet (UV) divergences and a QFT has to be regularized by modifying its short-distance or large energy momentum structure (momentum regularization is often used in this work). Since such a modification is somewhat arbitrary, it is necessary to verify that the resulting large-scale predictions are, at least to a large extent, short-distance insensitive. Such a verification relies on the renormalization theory and the corresponding renormalization group (RG). In this chapter, the essential steps of a proof of the perturbative renormalizability of the scalar φ4 QFT in dimension 4 are described. All the basic difficulties of renormalization theory, based on power counting, are already present in this simple example. The elegant presentation of Callan is followed, which makes it possible to prove renormalizability and RG equations (in Callan–Symanzik's (CS) form) simultaneously. The background of the discussion is effective QFT and emergent renormalizable theory. The concept of fine tuning and the issue of triviality are emphasized.

scholarly journals CONTINUITY OF THE FOUR-POINT FUNCTION OF MASSIVE $\varphi_{4}^{4}$-THEORY ABOVE THRESHOLD

2007 ◽  
Vol 19 (07) ◽  
pp. 725-747 ◽  
Author(s):  
CHRISTOPH KOPPER
Keyword(s):  
Renormalization Group ◽  
Integral Representations ◽  
Point Function ◽  
Renormalization Condition ◽  
Flow Equations ◽  
Physical Mass ◽  
Definition Of ◽  
Renormalization Theory

In this paper we prove that the four-point function of massive [Formula: see text]-theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.

INTRODUCTION TO THE NON-PERTURBATIVE RENORMALIZATION GROUP AND ITS RECENT APPLICATIONS

2000 ◽  
Vol 14 (12n13) ◽  
pp. 1249-1326 ◽  
Author(s):  
KEN-ICHI AOKI
Keyword(s):  
Renormalization Group ◽  
Order Approximation ◽  
High Energy ◽  
Group Method ◽  
Group Equation ◽  
Ferromagnetic Transition ◽  
Chiral Phase ◽  
Typical Application ◽  
Perturbative Renormalization ◽  
Renormalization Theory

We introduce the basic ideas and the framework of the non-perturbative renormalization group particularly for pedestrians using elementary examples. First we briefly review the history of the renormalization theory and the renormalization group. We will make it clear that the modern renormalization theory is constructed on the idea of the renormalization group and it is quite a new type of theory in physics. Then we derive the exact non-perturbative renormalization group equation and set up its systematic approximation method. The lowest order approximation called the local potential approximation is applied to scalar theories with the ferromagnetic transition and quantum mechanics with tunneling. We compare our results with other methods, and will show that the non-perturbative renormalization group method is promising since it gives fairly good results already in the lowest order approximation and it does not suffer any divergent series expansion. As a typical application in high energy physics, we analyze the dynamical chiral symmetry breaking in gauge theories and investigate the chiral phase structures. Our new method improves results by the ladder Schwinger–Dyson equation so that the physical results might be less gauge dependent.

The renormalization group and ultraviolet asymptotics

1979 ◽  
Vol 129 (11) ◽  
pp. 407 ◽  
Author(s):  
A.A. Vladimirov ◽  
D.V. Shirkov
Keyword(s):  
Renormalization Group
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