Relativistic Coulomb Green's function in $d$-dimensions

TL;DR

This paper derives the Green's functions for Dirac and Klein-Gordon equations in Coulomb potential across arbitrary dimensions using operator methods, analyzing their asymptotic behaviors.

Contribution

It introduces a novel derivation of relativistic Green's functions in arbitrary dimensions, expanding theoretical tools for quantum systems with Coulomb interactions.

Findings

Green's functions derived for arbitrary dimensions

Asymptotic behaviors analyzed in detail

Operator method applied successfully

Abstract

Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these Green's functions are considered in detail.