Ground state and the spin precession of the Dirac electron in counterpropagating plane electromagnetic waves

TL;DR

This paper derives the fundamental solution of the Dirac equation in a complex electromagnetic field composed of three standing waves, analyzing the ground state and spin precession of an electron in counterpropagating circularly polarized waves.

Contribution

It provides a new fundamental solution for the Dirac equation in a multi-wave electromagnetic field and analyzes electron ground state and spin dynamics in this context.

Findings

Fundamental solution expressed as a projection operator.

Analysis of ground state in a three-wave electromagnetic field.

Insights into spin precession in counterpropagating waves.

Abstract

The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency. Each standing wave consists of two eigenwaves with different complex amplitudes and opposite directions of propagation. The fundamental solution is obtained in the form of the projection operator defining the subspace of solutions to the Dirac equation. It is illustrated by the analysis of the ground state and the spin precession of the Dirac electron in the field of two counterpropagating plane waves with left and right circular polarizations. Interrelations between the fundamental solution and approximate partial solutions is discussed and a criterion for evaluating accuracy of approximate solutions is suggested.