On the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg

TL;DR

This paper analyzes and reconciles different derivations of Green functions in 5D off-shell electrodynamics within Stueckelberg's covariant framework, relating them to classical solutions and discussing retarded solutions in the invariant parameter.

Contribution

It clarifies and unifies various Green function derivations in 5D off-shell electrodynamics and connects them to established mathematical solutions.

Findings

Reconciliation of different Green function forms.

Relation to classical 5D wave equation solutions.

Physical justification for retarded Green functions.

Abstract

In previous paper derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter $\tau$). In this paper, we reconcile these derivations resulting in different explicit forms, and relate our results to the conventional fundamental solutions of linear 5D wave equations published in the mathematical literature. We give physical arguments for the choice of the Green function retarded in the fifth variable $\tau$.