A Z{sub 3} generalization of Pauli's principle, quark algebra and the Lorentz invariance
- Laboratoire de Physique Theorique de la Matiere Condensee, UMR CNRS 7600, Universite Pierre et Marie Curie, Tour 13-23, 5-eme etage, Bo Latin-Small-Letter-Dotless-I -carette 121, 4 Place Jussieu, 75005 Paris (France)
The fundamental difference between bosons and fermions is that they obey two alternative representations of the Z{sub 2} group, resulting in symmetric or anti-symmetric binary commutation relations. Our aim is to explore possibilities offered by ternary Z{sub 3} generalization commutation relations. This leads to cubic and ternary algebras which are a direct generalization of usual commutation relations, with Z{sub 3}-grading replacing the usual Z{sub 2}-grading. Properties and structure of such algebras are discussed, with special interest in a low-dimensional one, with two generators. Invariant cubic forms on such algebras are introduced, and it is shown how the SL(2,C) group arises naturally as the symmetry group preserving these forms. In the case of lowest dimension, with only two generators, it is shown how the cubic combinations of elements of the same Z{sub 3} grade behave like Lorentz spinors, while binary products of elements of this algebra with an element of the conjugate algebra behave like Lorentz vectors. The wave equation generalizing the Dirac operator to the Z{sub 3}-graded case is introduced, whose diagonalization leads to a third-order equation. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry obeyed by quark states.
- OSTI ID:
- 22075568
- Journal Information:
- AIP Conference Proceedings, Vol. 1483, Issue 1; Conference: 6. international school on field theory and gravitation 2012, Petropolis, RJ (Brazil), 23-27 Apr 2012; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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