On conformal invariant integrals involving spin one-half and spin-one particles

TL;DR

This paper evaluates conformal invariant integrals involving spin-1/2 and spin-1 particles, deriving the star-triangle relation for massless Yukawa theory and analyzing the three-point Green function in massless QED.

Contribution

It introduces a method to compute conformal invariant integrals with spins and derives new relations for massless Yukawa and QED theories.

Findings

Derived the star-triangle relation for massless Yukawa theory.

Determined the longitudinal part of the three-point Green function in massless QED.

Applied operator algebraic methods to evaluate Feynman integrals.

Abstract

We consider the evaluation of D-dimensional conformal invariant integrals which involve spin one-half and spin-one particles. The star-triangle relation for the massless Yukawa theory is derived, and the longitudinal part of the three-point Green function of massless QED is determined to the lowest order in position space. The operator algebraic method of calculating massless Feynman integrals is used for the evaluation.