Evaluation of nonrelativistic one-loop Feynman integrals by distributional methods

Abstract

In this paper, we use Feynman’s parameter formula and distribution theory in order to represent the integrals ∫Rn+1Πk=1l(it−(1)/(2m)|x−yk|2+μ)−1dt dx for m>0, μ>0, yk∈Rn, by definite integrals over simplices. We obtain explicit expressions in the cases of n=2 and n=l=3, respectively.