The Exact Electron Propagator in a Magnetic Field as the Sum over Landau Levels on a Basis of the Dirac Equation Exact Solutions

TL;DR

This paper derives the exact electron propagator in a magnetic field as a sum over Landau levels using Dirac equation solutions, aiding quantum process calculations in external fields, especially at moderate strengths.

Contribution

It provides a precise derivation of the electron propagator in a magnetic field as a sum over Landau levels based on exact Dirac solutions, enhancing computational methods in quantum field theory.

Findings

Exact propagator expressed as sum over Landau levels

Method applicable to moderate magnetic field strengths

Facilitates calculations in external active media

Abstract

The exact propagator for an electron in a constant uniform magnetic field as the sum over Landau levels is obtained by the direct derivation by standard methods of quantum field theory from exact solutions of the Dirac equation in the magnetic field. The result can be useful for further development of the calculation technique of quantum processes in an external active medium, particularly in the conditions of moderately large field strengths when it is insufficient to take into account only the ground Landau level contribution.