Charged massive vector boson propagator in a constant magnetic field in arbitrary $\xi$-gauge obtained using the modified Fock-Schwinger method

TL;DR

This paper presents an exact solution for the propagator of a charged massive vector boson in a constant magnetic field using a modified Fock-Schwinger method, applicable in arbitrary $\xi$-gauge, simplifying calculations and revealing new structural insights.

Contribution

The paper introduces a modified Fock-Schwinger method to derive the vector boson propagator in a magnetic field directly in momentum space for arbitrary $\xi$-gauge, improving computational efficiency and understanding.

Findings

Derived exact propagator in arbitrary $\xi$-gauge.

Reduced computational complexity compared to standard methods.

Revealed simple internal structures in the propagator expressions.

Abstract

We applied a recently published modified Fock-Schwinger (MFS) method to find the exact solution of the propagator equation for a charged vector boson in the presence of a constant magnetic field directly in the momentum space as a sum over Landau levels in arbitrary $\xi$-gauge. In contrast to the standard approaches for finding propagators, MFS method demonstrated several improvements in terms of computational complexity reduction and revealed simple internal structures in intermediate and final expressions, thus allowing to obtain new useful representations of the propagator.