2010/07/20 by В. М. Симулик, V. M. Simulik, Simulik, V. M. +3
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1007.3372
arxiv created 2010/07/20 · openalex publication_date 2010/07/20 · arxiv updated 2010/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.