A relativistic superalgebra in a generalized Schroedinger picture

TL;DR

This paper develops a relativistic superalgebra framework where time and space derivatives are not explicitly in particle operators, expressing supersymmetry and Hamiltonians for massive and massless particles with different spins using Lorentz group representations.

Contribution

It introduces a novel relativistic superalgebra formulation in a generalized Schrödinger picture, including new Hamiltonians for massless particles with spin zero and spin 1/2.

Findings

Constructed supersymmetry generators using Lorentz group representations

Developed new Hamiltonians for massless particles with specific spins

Extended superalgebra to include massless relativistic particles

Abstract

We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive relativistic particles with spin zero and spin-1/2 are expressed in terms of the principal series of the unitary representations of the Lorentz group. We also consider the massless case. New Hamilton operators are conctructed for the massless particles with spin zero and spin 1/2.