Dirac Particle in External Non-Abelian Gauge Field

The Green function of a Dirac particle in interaction with a non-Abelian SU(N) gauge fi…eld exactly and analytically determined via the path integral formalism by using the approach so-called “global projection.” The essential steps in the calculation are the choice of a convenient gauge (Lorentz gauge) and the introduction of two constraints, (related to space) and Grassmannian (related to Dirac matrices). Furthermore, it is shown that certain selected equations obtained during the integrations can also be classically derived.