Exact Green's function for fermions in an external Yang-Mills gauge field

TL;DR

This paper derives an exact Green's function for fermions interacting with a specific class of external non-Abelian gauge fields, specifically plane wave solutions to the Yang-Mills equations, advancing theoretical understanding in gauge field interactions.

Contribution

It provides an explicit analytical expression for the fermionic Green's function in a non-Abelian plane wave background, a novel exact solution in gauge theory.

Findings

Derived the exact Green's function for fermions in a non-Abelian plane wave field.

Extended theoretical tools for analyzing fermion-gauge field interactions.

Facilitated future calculations in non-Abelian gauge theories with external fields.

Abstract

We obtain the Green's function for fermions in an external non-Abelian gauge field with an $SU(N)$ symmetry group. As an external field, we examine the solution to the Yang-Mills equation presented as a plane wave on the light cone.