2013/11/07 by R. Huegele, Huegele, R., Z. E. Musielak +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1311.1672
21 pages
arxiv created 2013/11/07 · openalex publication_date 2013/11/07 · arxiv updated 2013/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equation for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon equations are also derived. In the non-relativistic limit the generalized Dirac equation gives the generalized Levy-Leblond equation and the generalized Pauli-Schrodinger equation. The main difference between the original and generalized Dirac equations is that the former and latter are obtained with zero and nonzero phase functions, respectively. Otherwise, both equations describe free elementary particles with spin 1/2, which have all other physical properties the same except their masses. The fact that the generalized Dirac equation describes elementary particles with larger masses is used to suggest that non-zero phase functions may account for the existence of three families of elementary particles in the Standard Model. This suggestion significantly differs from those previously made to account for the three families of particle physics.