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

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 $\mathrm{\Phi }$-bosons in an arbitrary $\xi$-gauge, expanded over Landau levels, are derived for the first time.