On the equation of motion for test particles in an ambient gravitational field as the Wong equation for a generalized gauge theory

In this note we demonstrate the equation of motion for test particles in an ambient gravitational field for the teleparallel theory of gravity, considered as a generalized gauge theory, using a computational scheme due to Feynman. It can be thought of as the Wong equation for a generalized gauge theory. The Wong and Lorentz equations become identical when the generators of a generalized non-abelian gauge theory are taken to be the local translation generators.