Position-space representation of charged particles' propagators in a constant magnetic field as an expansion over Landau levels

TL;DR

This paper derives position-space propagators for charged particles in a constant magnetic field, expanded over Landau levels, facilitating combined space-time and energy analysis in quantum field theory calculations.

Contribution

It provides a unique expansion of propagators over Landau levels that integrates space-time and energy perspectives, advancing position-space methods in QFT.

Findings

Derived position-space propagators as Landau level expansions

Expressions include rotational and Lorentz invariance factors

Facilitates calculations of loop diagrams in magnetic fields

Abstract

We have obtained propagators in the position space as an expansion over Landau levels for the charged scalar particle, fermion, and massive vector boson in a constant external magnetic field. The summation terms in the resulting expressions consisted of two factors, one being rotationally invariant in the 2-dimensional Euclidean space perpendicular to the direction of the field, and the other being Lorentz-invariant in the 1+1-dimensional space-time. The obtained representations are unique in the sense that they allow for the simultaneous study of the propagator from both space-time and energetic perspectives which are implicitly connected. These results contribute to the development of position-space techniques in QFT and are expected to be of use in the calculations of loop diagrams.