Symmetries of the relativistic two-boson system in external field

TL;DR

This paper explores how certain spacetime symmetries are preserved in a relativistic two-boson system under an external field, demonstrating that some symmetries can survive despite complex interactions.

Contribution

It introduces an ansatz that maintains the compatibility of mass-shell constraints, enabling the implementation of surviving isometries in the two-body wave equations.

Findings

Certain spacetime symmetries are preserved in the two-boson system.

The ansatz ensures compatibility of mass-shell constraints with external fields.

Surviving isometries can be incorporated into the wave equations.

Abstract

We investigate the survival of symmetries in a relativistic system of two mutually interacting bosons coupled with an external field, when this field is "strongly" translation invariant in some directions and additionally remains unchanged by other isometries of spacetime. Since the relativistic interactions cannot be composed additively, it is not a priori garanteed that the two-body system inherits all the symmetries of the external potential. However, using an ansatz which permits to preserve the compatibility of the mass-shell constraints in the presence of the field, we show how "surviving isometries" can actually be implemented in the two-body wave equations.