On the Fermi - Bose duality of the Dirac equation with nonzero mass

TL;DR

This paper demonstrates that the Dirac equation with nonzero mass can describe both fermions and bosons, revealing new bosonic symmetries and a spin 1 Poincare symmetry through symmetry analysis and Clifford algebra.

Contribution

It introduces a novel symmetry analysis showing the Dirac equation's capacity to describe spin 1 bosons, expanding its physical interpretation.

Findings

Discovery of bosonic symmetries in the Dirac equation

Identification of a spin 1 Poincare symmetry

Use of extended Clifford algebra for proofs

Abstract

We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2, but also bosons of spin 1. The new bosonic symmetries of the Dirac equation in both the Foldy -- Wouthuysen and the Pauli -- Dirac representations are found. Among these symmetries (together with the 32-dimensional pure matrix algebra of invariance) the new, physically meaningful spin 1 Poincare symmetry of equation under consideration is proved. In order to carry out the corresponding proofs a 64-dimensional extended real Clifford -- Dirac algebra is put into consideration.