2014/05/26 by Christian Rakotonirina, Rakotonirina, Christian · 1 citation
Physics and Astronomy · #15-06 #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Quantum and Classical Electrodynamics #msc:15-06 #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1405.7668
68 pages, Dissertation, Mémoire d'Habilitation à Diriger des Recherches, in French
arxiv created 2014/05/26 · openalex publication_date 2014/05/26 · arxiv updated 2014/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct two sets of representations of the Dirac equation. They transform themselves from one to another in multiplying by the tensor commutation matrix (TCM) 2⊗ 2. The Gauss matrix can lead us to the Cholesky decomposition. The TCMs can be used in order to obtain different transforms of some matrix equations to linear matrix equations of the form AX=B. A TCM n⊗ n is expressed in terms of the n⊗ n-Gell-Mann matrices. In order to generalize this expression to which of TCMs n⊗ p, we introduced what we call rectangle Gell-Mann matrices. The electric charge operator (ECO) for eight leptons and quarks of the Standard Model (SM) of a same generation proposed by Zenczykowski is expressed in terms of the TCM 2⊗ 2. An ECO including all the fermions of the SM is constructed in terms of TCM 4⊗ 4. Then the eigenvalues of a TCM take sense.