Integrable relativistic systems given by Hamiltonians with momentum-spin-orbit coupling

TL;DR

This paper studies the evolution of relativistic particles with spin under Hamiltonians that include momentum-spin-orbit coupling, solving the equations explicitly using elliptic functions.

Contribution

It provides explicit integration of Hamiltonian equations for relativistic particles with spin, including cases with momentum-spin-orbit coupling, expressed via elliptic functions.

Findings

Explicit solutions for relativistic particles with spin

Hamiltonian equations integrated in quadratures

Solutions expressed in elliptic functions

Abstract

In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We integrate the corresponding Hamiltonian equations in quadratures and express their solutions in terms of elliptic functions.