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

TL;DR

This paper derives the equation of motion for test particles in a gravitational field within teleparallel gravity, framing it as a Wong equation for a generalized gauge theory, highlighting its gauge-theoretic structure.

Contribution

It demonstrates the equation of motion in teleparallel gravity as a Wong equation, connecting gravitational dynamics with gauge theory concepts using Feynman's computational scheme.

Findings

Equation of motion matches Wong equation in gauge theory context

Unifies gravitational and gauge interactions in a generalized framework

Shows equivalence of Wong and Lorentz equations under specific generators

Abstract

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.