Some examples of uses of Dirac equation and its generalizations in particle physics

TL;DR

This paper explores various generalizations and applications of the Dirac equation, including its use in describing particles like electrons, muons, and quarks, and examines extended symmetries for advanced particle physics insights.

Contribution

It introduces new generalizations of the Dirac equation, such as the Dirac-Gursey-Lee and higher-dimensional forms, for improved modeling of particle properties and confinement phenomena.

Findings

Solutions can approximate quark states inside hadrons

Extended symmetries facilitate analysis of solutions

Generalizations may aid in particle physics research

Abstract

Applications of the Dirac equation with an anomalous magnetic moment are considered for description of characteristics of electrons, muons and quarks. The Dirac equation with four-dimensional scalar and vector potentials is reduced to a form suitable for a numerical integration. When a certain type of the potential is chosen, solutions can approximate quark states inside hadrons. In view of complicated behaviour of quarks in a confinement domain some generalizations are considered such as the Dirac-Gursey-Lee equation, the Dirac equation in a five-dimensional Minkowski space, the Dirac equation in a quantum phase space. Extended symmetries for the Dirac equation and its generalizations are considered, which can be used for investigation of properties of solutions of these equations and subsequent applications in particle physics.