Use of group theory and Clifford algebra in the study of generalized Dirac equation for particles with arbitrary spin

TL;DR

This paper develops a generalized Dirac equation for particles with arbitrary spin using group theory and Clifford algebra, ensuring Lorentz invariance and reducing to known equations for specific spins.

Contribution

It introduces a new form of the Dirac equation applicable to particles of any spin, expanding the theoretical framework for relativistic quantum particles.

Findings

Generalized Dirac equation for arbitrary spin particles derived

Equation reduces to known forms for half-integer and scalar spins

Provides a unified mathematical description for various spin particles

Abstract

Using condition of relativistic invariance, group theory and Clifford algebra the component Lorentz invariance generalized Dirac equation for a particle with arbitrary mass and spin is suggested, where In the case of half-integral spin particles, this equation is reduced to the sets of two-component independent matrix equations. It is shown that the relativistic scalar and integral spin particles are described by component equation.