Linear combinations of radiative corrections: Renormalization group and renormalization theory

1970 ◽  
Vol 65 (4) ◽  
pp. 617-636
Author(s):  
A. Visconti
Keyword(s):  
Renormalization Group ◽  
Radiative Corrections ◽  
Linear Combinations ◽  
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.

scholarly journals Renormalization group summation with heavy fields

2018 ◽  
Vol 96 (11) ◽  
pp. 1205-1208
Author(s):  
D.G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Explicit Calculation ◽  
Radiative Corrections ◽  
Group Equation ◽  
Physical Processes ◽  
The Masses ◽  
Massive Fields

The summation of logarithmic contributions to perturbative radiative corrections in physical processes through use of the renormalization group equation has proved to be a useful way of enhancing the information one can obtain from explicit calculation. However, it has proved difficult to perform this summation when massive fields are present. In this work we point out that if the masses involved are quite large, the decoupling theorem of Symanzik and of Appelquist and Carazzone can be used to make the summation of logarithms possible.

scholarly journals Renormalization scheme dependence and renormalization group summation

2018 ◽  
Vol 96 (2) ◽  
pp. 233-240 ◽  
Author(s):  
F.A. Chishtie ◽  
D.G.C. McKeon
Keyword(s):  
Free Energy ◽  
Renormalization Group ◽  
Effective Action ◽  
Sum Rules ◽  
Scale Parameter ◽  
Higher Order ◽  
Renormalization Scheme ◽  
Radiative Corrections ◽  
Renormalization Scale ◽  
Running Coupling

We consider logarithmic contributions to the free energy, instanton effective action, and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all dependence on the renormalization scale parameter μ cancels. The renormalization scheme dependence in these processes is examined, and a renormalization scheme is found in which the effect of higher-order radiative corrections is absorbed by the behaviour of the running coupling.

scholarly journals RENORMALIZATION GROUP IMPROVED RADIATIVE CORRECTIONS TO THE SUPERSYMMETRIC HIGGS BOSON MASSES

1995 ◽  
Vol 10 (40) ◽  
pp. 3129-3137 ◽  
Author(s):  
A.V. GLADYSHEV ◽  
D.I. KAZAKOV
Keyword(s):  
Renormalization Group ◽  
Higgs Boson ◽  
Effective Potential ◽  
Top Quark ◽  
Higgs Mass ◽  
Radiative Corrections ◽  
Mass Dependence ◽  
The One ◽  
Top Mass

The one-loop radiative corrections to the Higgs boson potential in the MSSM, originating from the top quark and squark loops, are summed in the leading log approximation using the renormalization group (RG). The RG improved effective potential is minimized and the corrections to the CP-odd and CP-even Higgs boson masses are calculated. The resulting masses exhibit smoother top mass dependence than those calculated without RG summation. We have also found that for preferable values of the top mass the light Higgs mass does not exceed 100 GeV.

Sign in / Sign up

Export Citation Format

Share Document