Relativistic wave equation for one spin-1/2 and one spin-0 particle

TL;DR

This paper develops a novel relativistic wave equation for a two-particle system consisting of one spin-1/2 and one spin-0 particle with unequal masses, using an extended group theoretical framework.

Contribution

It introduces a new approach extending the $SL(2,C)$ group to $Sp(4,C)$ for modeling two-body relativistic interactions.

Findings

Wave equation incorporating Lorentz-scalar and Lorentz-vector potentials

Applicable to systems with unequal masses

Provides a group-theoretic foundation for two-body relativistic quantum mechanics

Abstract

A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with the Lorentz-scalar and Lorentz-vector potential interactions for the system of one spin-1/2 and one spin-0 particle with unequal masses is constructed.