Relativistic two-boson system in presence of electromagnetic plane waves

TL;DR

This paper develops explicit covariant wave equations for a relativistic two-boson system under the influence of two counter-propagating electromagnetic plane waves, accounting for mutual interactions and reducing the problem to five degrees of freedom.

Contribution

It introduces a novel set of coupled covariant wave equations for a two-boson system in a specific electromagnetic field configuration, including explicit constants of motion.

Findings

Explicit covariant wave equations derived for the system.

Reduction to a five-degree-of-freedom problem.

Inclusion of mutual interactions and field effects.

Abstract

The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem involving five degrees of freedom.