Divergence Free QED Lagrangian in (2 + 1)-Dimensional Space-Time with Three Different Regularization Prescriptions - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.10, October 2018

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

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DOI: 10.4236/jamp.2018.610175 604 Downloads 1,256 Views

Author(s)

M. Forkan¹, M. Abul Mansur Chowdhury²

Affiliation(s)

¹Department of Mathematics, University of Chittagong, Chittagong, Bangladesh.
²JNI Research Centre for Mathematical and Physical Sciences, University of Chittagong, Chittagong, Bangladesh.

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.

KEYWORDS

Operator Regularization, Dimensional Regularization, Feynman Diagrams in QED, Path-Integral Method, Background Field Quantization and Generating Functional

Share and Cite:

Forkan, M. and Chowdhury, M. (2018) Divergence Free QED Lagrangian in (2 + 1)-Dimensional Space-Time with Three Different Regularization Prescriptions. Journal of Applied Mathematics and Physics, 6, 2067-2086. doi: 10.4236/jamp.2018.610175.

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