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- Title
GENERALIZED DIRAC'S EQUATION AND ITS Z<sub>3</sub>-GRADED SYMMETRIES.
- Authors
KERNER, RICHARD
- Abstract
The present article investigates the Lorentz-Poincaré covariance properties of the generalized Dirac equation for quarks endowed, besides the half-integer spin, with "color", a Z3-graded discrete variable. Thus to the the Z2 X-Z2 symmetry of the Dirac equation, corresponding to the double-valued spin variable and the charge conjugation imposing the particle-antiparticle duality, we shall add an extra Z3 symmetry describing the color variable. The difference with currently accepted QCD is that instead of three Dirac spinors carrying different colors, the generalized equation introduced in ([14], [6], [7], [9]) attributes color variables to double-valued Pauli spinors first, and the charge conjugation next, creating 12-component wave functions. The 3 X 3 generators of the SU(3) color Lie algebra appear spontaneously. The invariance under Z3-graded spinorial representation of the Lorentz-Poincaré algebra is investigated. It leads to the enlargement of symmetry by introduction of new degrees of freedom, corresponding to extra Z2-Z3 symmetry, which we attribute to the existence of three families with two avors in each ([12], [13]). The orbital representation of Z3-graded Lorentz-Poincaré algebra is constructed using the enlarged Z3-graded Minkowskian space-time M4 X Z3. Matrix and differential operator representations are presented in extenso, along with the generalized Casimir operators.
- Subjects
DIRAC equation; SYMMETRIES (Quantum mechanics); LORENTZ groups; CONTINUOUS groups; SPINORS
- Publication
Revue Roumaine de Mathematiques Pures et Appliquees, 2020, Issue 4, p457
- ISSN
0035-3965
- Publication type
Article