Lorentz Invariant Equations for Multiplets and Their Gauge

TL;DR

This paper investigates Lorentz invariant equations for a two-particle spin multiplet, revealing new gauge invariances that emerge only when particles are considered together, and analyzes their solution properties.

Contribution

It introduces kinematical gauge transformations specific to multiplet equations, absent in single-particle cases, expanding understanding of gauge invariance in relativistic quantum equations.

Findings

Identifies three groups of gauge transformations for the multiplet equations.

Shows gauge invariance is absent when particles are considered separately.

Analyzes basic properties of solutions to these multiplet equations.

Abstract

This paper explores the existence of kinematical gauge transformations for Lorentz invariant equations which describe a multiplet of two spin $\frac{1}{2}$ particles. For this multiplet the additional gauge invariance can be in form of three different groups of transformation. This gauge is absent when the particles are treated separately. Some basic properties of the solutions for these "multiplet equations" are analyzed.