Coordinate-space representation of a charged scalar particle propagator in a constant magnetic field expanded as a sum over the Landau levels

Abstract

Abstract A coordinate-space representation for a charged scalar particle propagator in a constant magnetic field was obtained as a series over the Landau levels. Using the recently developed modified Fock–Schwinger method, an intermediate expression was constructed and symmetrized, thus, allowing for factorization of the series terms into two factors. The first one, a sum of Bessel functions, depends on time and z-coordinate, where the z-axis is chosen to be a direction of the magnetic field, and has a structure similar to the propagator of a free field. The second one, a product of a Laguerre polynomial and a damping exponential, depends on x, y-coordinates, which form a plane perpendicular to the direction of the magnetic field, and ensures the localized propagation in the x, y-plane.