1999/09/16 by A. A. Ketsaris, А. А. Кецарис, Ketsaris, A. A.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #advanced mathematical theories #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9909053
26 pages, no figures, uses revtex, submitted to Phys.Rev.D
arxiv created 1999/09/16 · openalex publication_date 1999/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to derive quantum mechanics equations from structure equations of the specified algebras. A new interpretation of the wave function is given as differential of the action vector. A generalization of the Dirac equation for 8-component wave function is derived. It is interpreted as the equation for two leptons of the same generation. A procedure of the approximate description of free leptons is formulated. The generalized equation of quantum mechanics is reduced to the Dirac, Pauli and Schrödinger equations by the sequential use of this procedure. We explain the existence of three lepton generations.