Massive Relativistic Particle Models with Bosonic Counterpart of Supersymmetry

TL;DR

This paper develops massive relativistic particle models in four-dimensional Minkowski space extended by Weyl spinors, revealing bosonic counterparts of supersymmetry and deriving associated quantum fields with specific equations of motion.

Contribution

It introduces new particle models with bosonic analogs of supersymmetry for N=1 and N=2, leading to novel quantum fields and equations of motion for higher spins.

Findings

N=1 model yields bosonic chiral superfield counterparts satisfying Klein-Gordon equation.

Massless case fields satisfy Fierz-Pauli equations.

N=2 model produces free massive higher spin fields obeying Bargmann-Wigner equations.

Abstract

We consider the massive relativistic particle models on fourdimensional Minkowski space extended by $N$ commuting Weyl spinors for N=1 and N=2. The N=1 model is invariant under the most general form of bosonic counterpart of simple D=4 supersymmetry, and provides after quantization the bosonic counterpart of chiral superfields, satisfying Klein--Gordon equation. In massless case these fields do satisfy the Fierz-Pauli equations. For N=2 we obtain after quantization the free massive higher spin fields for arbitrary spin satisfying linear Bargman--Wigner equations. Finally the problem of statistics in presented framework for half--integer classical spin fields is discussed.