The Dirac equation near centenary: a contemporary introduction to the Dirac equation consideration

Source abstract

Abstract More then 35 approaches to the Dirac equation derivation are presented. Various physical principles and mathematical methods are used. A review of well-known and not enough known contributions to the problem is given, unexpected and unconventional derivations are presented as well. Three original approaches to the problem suggested by the author are considered: (i) generalization of H. Sallhofer derivation, (ii) obtaining of massless Dirac equation from the Maxwell equations in a maximally symmetrical form, (iii) derivation of the Dirac equation with nonzero mass from 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 is established.