Gaussian as test functions in Operator Valued Distribution formulation of QED
Abstract
As shown by Epstein and Glaser, the operator valued distribution (OPVD) formalism permits to obtain a non-standard regularization scheme which leads to a divergences-free quantum field theory. We show, with the example of a scalar quantum electrodynamics theory, that Gaussian functions may be used as test functions in this approach. After a short recall about the OPVD formalism in 3+1-dimensions, Gaussian functions and Harmonic Hermite-Gaussian functions are used as test functions. The vacuum fluctuation, Feynman propagators and a study about loop convergence with the example of the tadpole diagram are given. The approach is extended to Quantum Electrodynamics. Calculations concerning triangle anomaly and Ward-Takahashi identity are performed in the framework of the method.
Cite
@article{arxiv.1808.00797,
title = {Gaussian as test functions in Operator Valued Distribution formulation of QED},
author = {Hasimbola Damo Emile Randriamisy and Raoelina Andriambololona and Hanitriarivo Rakotoson and Ravo Tokiniaina Ranaivoson and Roland Raboanary},
journal= {arXiv preprint arXiv:1808.00797},
year = {2018}
}
Comments
12 pages