Supersymmetric Relativistic Quantum Mechanics

TL;DR

This paper explores formulating supersymmetric relativistic quantum mechanics at the single-particle level using equations of motion and matrix operators, aiming to realize supersymmetry before filling the Dirac sea.

Contribution

It introduces a matrix formulation for supersymmetry operators in relativistic quantum mechanics, focusing on single-particle realization prior to second quantization.

Findings

Supersymmetry can be realized at the single-particle level.

Matrix formulation effectively expresses supersymmetry generators and fields.

The approach precedes the filling of the Dirac sea.

Abstract

We present an attempt to formulate the supersymmetric and relativistic quantum mechanics in the sense of realizing supersymmetry on the single particle level, by utilizing the equations of motion which is equivalent to the ordinary 2nd quantization of the chiral multiplet. The matrix formulation is used to express the operators such as supersymmtry generators and fields of the chiral multiplets. We realize supersymmetry prior to filling the Dirac sea.