A simple expression for the four-point scalar function from Gaussian integrals and Fourier transform
Abstract
Recasting the -point one loop scalar integral from Feynman to Schwinger parameters gives an integrand with a Gaussian form. By application of a Fourier transform, it is easy to derive explicit expressions for the two, three and four-point functions. The Fourier transformation disentangles singularities in the complex plane and extract their contribution as two-point functions in two dimensions. We explicitly derive a one dimensional expression for the (4D) four-point function whose integrand involves only square root and arcsine functions. This report is a condensed version of the approach developed in \cite{Benhaddou2016} which does not make use of probabilistic jargon.
Cite
@article{arxiv.1711.08794,
title = {A simple expression for the four-point scalar function from Gaussian integrals and Fourier transform},
author = {Kamel Benhaddou},
journal= {arXiv preprint arXiv:1711.08794},
year = {2017}
}
Comments
This is an abridged version of arXiv:1603.05204 that focuses on the 4D four-point function and that does not use a probabilistic language