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We applied a recently published modified Fock-Schwinger (MFS) method to findthe exact solution of the propagator equation for a charged vector boson in thepresence of a constant magnetic field directly in the momentum space as a sumover Landau levels in arbitrary $\xi$-gauge. In contrast to the standardapproaches for finding propagators, MFS method demonstrated severalimprovements in terms of computational complexity reduction and revealed simpleinternal structures in intermediate and final expressions, thus allowing toobtain new useful representations of the propagator.

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