Produit tensoriel de Matrices en Théorie de DIRAC
Faculte Des Sciences - Physiques et Applications - None ()
Resume
Properties of tensorial product of matrices are constructed. These properties are used to study factorizations of the real Clifford algebras of the square matrices, by tensorial product of matrices. Applying these factorizations, we found a way to get, from Pauli’s matrices, twelve systems and only twelve; each of them is formed of four matrices coefficients of a Dirac’s equation. We looked for solutions of these twelve equations for free fundamental leptons. These twelve equations can be constructed by quantification of the relativistic energy-momentum relation. We introduced a notion that we called equivalence of particles. Then, the equivalence between free fundamental fermions are studied. Finally, we demonstrated the equivalence between Dirac’s equation and Hestenes’s, to try to look for hidden physical properties.