Some statistical aspects of the spinor field Fermi-Bose duality

TL;DR

This paper explores the statistical properties of the Fermi-Bose duality in spinor fields, demonstrating that the Dirac equation can describe both fermionic and bosonic states using a specific 29-dimensional Clifford-Dirac algebra.

Contribution

It introduces a novel algebraic framework to prove the Fermi-Bose duality of the Dirac equation and discusses its statistical implications.

Findings

Dirac equation describes both fermionic and bosonic states

Fermi-Bose duality is supported by symmetry and conservation laws

Statistical aspects of duality are analyzed

Abstract

The structure of 29-dimensional extended real Clifford-Dirac algebra, which has been introduced in our paper Phys. Lett. A, 2011, 375, 2479, is considered in brief. Using this algebra, the property of Fermi-Bose duality of the Dirac equation with nonzero mass is proved. It means that Dirac equation can describe not only the fermionic but also the bosonic states. The proof of our assertion based on the examples of bosonic symmetries, solutions and conservation laws is given. Some statistical aspects of the spinor field Fermi-Bose duality are discussed.