The Dirac Equation Near Centenary: a Contemporary Introduction to the Dirac Equation Consideration

TL;DR

This paper reviews over 35 methods for deriving the Dirac equation, introduces three original approaches, and discusses the equation's significance in modern physics, highlighting new features and establishing criteria for derivation usefulness.

Contribution

It presents three novel derivations of the Dirac equation and evaluates their significance, expanding understanding of its foundational role in physics.

Findings

New derivation methods for the Dirac equation are demonstrated.

Original approaches reveal additional features of the Dirac equation.

Criteria for assessing the usefulness of derivation methods are established.

Abstract

More then 35 approaches to the Dirac equation derivation are presented. The various physical principles and mathematical methods are used. A review of well-known and not enough known contributions to the problem is given, the unexpected and unconventional derivations are presented as well. Three original approaches to the problem suggested by the author are considered as well. They are (i) the generalization of H. Sallhofer derivation, (ii) the obtaining of the massless Dirac equation from the Maxwell equations in maximally symmetrical form, (iii) the derivation of the Dirac equation with nonzero mass from the relativistic canonical quantum mechanics of the fermion-antifermion spin s=1/2 doublet. Today we are able to demonstrate new features of our derivations given in original papers. In some sense the important role of the Dirac equation in contemporary theoretical physics is demonstrated. A criterion for the usefulness of one or another derivation of the Dirac equation has been established