Divergence Free QED Lagrangian in (2 + 1)-Dimensional Space-Time with Three Different Regularization Prescriptions

M Forkan,M Abul Mansur Chowdhury

doi:10.4236/jamp.2018.610175

Abstract

Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams and non-perturbative means using Path-integral method. Operator regularization (OR) is one of the exceptional methods to study gauge theories because of its two-fold prescriptions. That means in OR two types of prescriptions have been introduced, which gives us the opportunity to check the result in self consistent way. In an earlier paper, we have evaluated basic QED loop diagrams in (3 + 1) dimensions using the both methods of OR and Dimensional regularization (DR). Then all three results have been compared. It is seen that the finite part of the result is almost same. In this paper, we are interested to evaluate the same basic loop diagrams in (2 + 1) space-time dimensions, because of two reasons: the main reason in (2 + 1) space-time dimensions, these loops diagrams are finite, on other hand, there are divergences in (3 + 1) space-time dimensions and the other reason is to see validity of using OR to evaluate Feynman loop diagrams in all dimensions. Here we have used both prescriptions of OR and DR to evaluate the basic loop diagrams and compared the results. Interestingly the results are almost same in all cases.

Highlights

That means Operator regularization (OR) is mainly a path integral method but at one stage there is an option to consider the term as a factor for operator for loop diagrams
Radiative corrections in quantum field theory are very important for renormalization of a theory
Operator regularization (OR) method had been prescribed to overcome some of these problems

Summary

Introduction

Gauge theories [1]-[7] describe the interactions of all known forces such as elec-. M. In non-perturbative method, we expand the generating function in terms of path integrals, using different techniques we try to renormalize the theory to find the different features of the particles involved in the interactions. Operator regularization (OR) method is one of the best non-perturbative methods to study gauge theories. Operator regularization method was prescribed by D.G.C. McKeon et al [15] [16] [17] to study gauge theories non-perturbatively. In an earlier paper [20] we have described OR method in both ways and evaluated one-loop Feynman diagrams in QED in (3 + 1) space-time dimensions. We have used the same method to evaluate the basic QED one-loop Feynman diagrams in (2 + 1) space-time dimensions to see the basic difference between finite and infinite loop integrals. Because in (3 + 1) dimensions, the loop integrals are divergent, on the other hand, in (2 + 1) dimensions, the loop integrals are finite

Operator Regularization Prescription

M 2 1 2

One-Loop Generating Functional and Loop Corrections for External Boson Lines

Conclusion