scholarly journals Towards perturbative renormalization of ϕ2(iϕ)ϵ quantum field theory

2021 ◽  
Vol 104 (8) ◽  
Author(s):  
Alexander Felski ◽  
Carl M. Bender ◽  
S. P. Klevansky ◽  
Sarben Sarkar
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Perturbative Renormalization

Renormalization Group: From a general concept to numbers

2019 ◽  
pp. 69-80
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
General Concept ◽  
Quantum Field ◽  
Fixed Dimension ◽  
Perturbative Renormalization ◽  
Borel Transformation

Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples where this concepts fails. To deal with such a situation, a new tool has been invented: the renormalization group. In the framework of effective quantum field theory, a perturbative renormalization group has been formulated. Its implementation has led to the discovery of fixed points as zeros of beta functions, and calculations of critical exponents of a class of macroscopic phase transitions in the form of Wilson–Fisher epsilon or fixed dimension expansions. These expansions being divergent, they could summed by methods based on the Borel transformation and the determination of the large order behaviour of perturbation theory.

scholarly journals Perturbative Renormalization by Flow Equations

2003 ◽  
Vol 15 (05) ◽  
pp. 491-558 ◽  
Author(s):  
Volkhard F. Müller
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Quantum Field ◽  
Flow Equations ◽  
Yang Mills ◽  
Perturbative Renormalization

In this article a self-contained exposition of proving perturbative renormalizability of a quantum field theory based on an adaption of Wilson's differential renormalization group equation to perturbation theory is given. The topics treated include the spontaneously broken SU(2) Yang–Mills theory. Although mainly a coherent but selective review, the article contains also some simplifications and extensions with respect to the literature.

scholarly journals Non-perturbative renormalization flow in quantum field theory and statistical physics

2002 ◽  
Vol 363 (4-6) ◽  
pp. 223-386 ◽  
Author(s):  
Jürgen Berges ◽  
Nikolaos Tetradis ◽  
Christof Wetterich
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Statistical Physics ◽  
Quantum Field ◽  
Perturbative Renormalization

scholarly journals The Validity of Dimensional Regularization Method on Fractal Spacetime

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yong Tao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Electrodynamics ◽  
Regularization Method ◽  
Integral Formula ◽  
Dimensional Regularization ◽  
Topological Spaces ◽  
Quantum Field ◽  
Fractal Measure ◽  
Perturbative Renormalization

Svozil developed a regularization method for quantum field theory on fractal spacetime (1987). Such a method can be applied to the low-order perturbative renormalization of quantum electrodynamics but will depend on a conjectural integral formula on non-integer-dimensional topological spaces. The main purpose of this paper is to construct a fractal measure so as to guarantee the validity of the conjectural integral formula.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Some remarks on a deformed quantum field theory

2002 ◽  
Author(s):  
Marco Aurelio Do Rego Monteiro ◽  
V. B. Bezerra ◽  
E. M.F. Curado
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field
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