Path Integration in QCD with Arbitrary Space-Dependent Static Color Potential

Abstract

We perform path integral for a quark (antiquark) in the presence of an arbitrary space-dependent static color potential A^a_0(x)(=-\int dx E^a(x)) with arbitrary color index a=1,2,...8 in SU(3) and obtain an exact non-perturbative expression for the generating functional. We show that such a path integration is possible even if one can not solve the Dirac equation in the presence of arbitrary space-dependent potential. It may be possible to further explore this path integral technique to study non-perturbative bound state formation.