Green Functions For Wave Propagation on a 5D manifold and the Associated Gauge Fields Generated by a Uniformly Moving Point Source

TL;DR

This paper derives Green functions for 5D gauge fields in flat spacetimes, providing solutions for a moving point source, and explores their implications for wave propagation in higher-dimensional manifolds.

Contribution

It presents explicit solutions and Green functions for 5D gauge fields generated by a moving point source in different flat spacetime metrics.

Findings

Green functions are consistent with direct solutions for uniform motion.

Explicit solutions for gauge fields in (4,1) and (3,2) metrics.

Enhanced understanding of wave propagation in 5D manifolds.

Abstract

Gauge fields associated with the manifestly covariant dynamics of particles in (3,1) spacetime are five-dimensional. We provide solutions of the classical 5D gauge field equations in both (4,1) and (3,2) flat spacetime metrics for the simple example of a uniformly moving point source. Green functions for the 5D field equations are obtained, which are consistent with the solutions for uniform motion obtained directly from the field equations with free asymptotic conditions.