TITLE:
Divergence Free QED Lagrangian in (2 + 1)-Dimensional Space-Time with Three Different Regularization Prescriptions
AUTHORS:
M. Forkan, M. Abul Mansur Chowdhury
KEYWORDS:
Operator Regularization, Dimensional Regularization, Feynman Diagrams in QED, Path-Integral Method, Background Field Quantization and Generating Functional
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.10,
October
25,
2018
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.