A new approach to the relativistic treatment of the fermion-boson system, based on the extension of the SL(2,C) group

TL;DR

This paper introduces a novel relativistic wave equation for fermion-boson systems using an extended group symmetry, accurately capturing interactions and kinematics, and aligning with known limits.

Contribution

It extends the SL(2,C) group to Sp(4,C) to develop a new relativistic wave equation for spin-1/2 and spin-0 particles, incorporating complex interaction potentials.

Findings

The new equation includes Lorentz-vector and tensor potentials.

It correctly describes relativistic kinematics.

It reduces to known one-particle limits.

Abstract

A new technique for constructing the relativistic wave equation for the two-body system composed of the spin-1/2 and spin-0 particles is proposed. The method is based on the extension of the SL(2,C) group to the Sp(4,C) one. The obtained equation includes the interaction potentials, having both the Lorentz-vector and Lorentz-tensor structure, exactly describes the relativistic kinematics and possesses the correct one-particle limits. The comparison with results of other approaches to this problem is discussed.