Propagators of charged particles in an external magnetic field, expanded over Landau levels

TL;DR

This paper derives formulas for charged particle propagators in a magnetic field expanded over Landau levels, facilitating calculations in electroweak processes involving external magnetic fields.

Contribution

It introduces the first derivation of propagators for Standard Model charged W- and scalar Phi-bosons expanded over Landau levels in an arbitrary gauge.

Findings

Formulas for propagators in Landau level expansion are provided.

The derivations are applicable to electroweak process calculations in magnetic fields.

The work covers arbitrary gauge choices for the propagators.

Abstract

Various forms of expressions for the propagators of charged particles in a constant magnetic field that should be used for investigations of electroweak processes in external uniform magnetic field are discussed. Formulas for the propagators of the Standard Model charged $W$- and scalar $\Phi$-bosons in an arbitrary $\xi$-gauge, expanded over Landau levels, are derived for the first time.