scholarly journals Small distance behaviour in field theory and power counting

1970 ◽  
Vol 18 (3) ◽  
pp. 227-246 ◽  
Author(s):  
K. Symanzik
Keyword(s):  
Field Theory ◽  
Small Distance ◽  
Power Counting

scholarly journals The one-loop tadpole in the geoSMEFT

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Tyler Corbett
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Power Counting ◽  
Leading Order ◽  
The Standard Model ◽  
The One ◽  
Near Future ◽  
Geometric Formulation

Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.

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.

The Principles of Renormalisation

2021 ◽  
pp. 304-328
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Power Counting ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Green Functions ◽  
Quantum Field Theories ◽  
Quantum Field

Loop diagrams often yield ultraviolet divergent integrals. We introduce the concept of one-particle irreducible diagrams and develop the power counting argument which makes possible the classification of quantum field theories into non-renormalisable, renormalisable and super-renormalisable. We describe some regularisation schemes with particular emphasis on dimensional regularisation. The renormalisation programme is described at one loop order for φ‎4 and QED. We argue, without presenting the detailed proof, that the programme can be extended to any finite order in the perturbation expansion for every renormalisable (or super-renormalisable) quantum field theory. We derive the equation of the renormalisation group and explain how it can be used in order to study the asymptotic behaviour of Green functions. This makes it possible to introduce the concept of asymptotic freedom.

scholarly journals Power counting and Wilsonian renormalization in nuclear effective field theory

2016 ◽  
Vol 25 (05) ◽  
pp. 1641007 ◽  
Author(s):  
Manuel Pavón Valderrama
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Nuclear Physics ◽  
High Energy ◽  
Effective Field ◽  
Power Counting ◽  
Low Energy ◽  
Field Theories ◽  
Nuclear Forces

Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.

scholarly journals Group field theory renormalization in the 3D case: Power counting of divergences

2009 ◽  
Vol 80 (4) ◽  
Author(s):  
Laurent Freidel ◽  
Razvan Gurau ◽  
Daniele Oriti
Keyword(s):  
Field Theory ◽  
Power Counting ◽  
Group Field Theory
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