Abstract
The objective of this paper is to introduce first the concept of Dirac oscillator in the one particle case, and generalize it to the n-body problem. Considering then the specific case when n = 3 we obtain the spectrum of the three quark problem when they interact through a Dirac oscillator type of potential. This spectrum does not look like the one of the baryons and even has an infinitely degenerate ground state, but if we generalize the Hamiltonian to include some of the integrals of motion of the many body Dirac oscillator, we do get a spectrum that resembles the one of non-strange baryons.
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References
M. Moshinsky and A. Szczepaniak, J. Phys. A: Math. Gen. 22, L817 (1989).
C. Quesne and M. Moshinsky, J. Phys. A: Math. Gen. 23, 2263 (1990).
D. Ito, K. Mori, E. Carrière, Nuevo Cimento 51A, 1119 (1964)
P.A. Cook, Lett. Nuovo Cimento 1, 419 (1971).
L.I. Schiff, Quantum Mechanics (McGraw-Hill Book Co. N.Y.) Third Edition 1968 pp. 472-490.
Y.S. Kim and M.E. Noz, “Theory and Applications of the Poincaré Group” (D. Reidel Publishing Co. Dordrecht 1986).
A.O. Barut and S. Komy, Fortsch. Phys. 33, 6 (1985)
A.O. Barut and G.L. Strobel, Few-body Systems 1, 167 (1986).
M. Moshinsky, G. Loyola, C. Villegas, J. Math. Phys. 32, 373 (1991).
M. Moshinsky and A. Sanchez, Rev. Mex. Fís. 34, 511 (1988).
M. Moshinsky, G. Loyola, A. Szczepaniak, C. Villegas, N. Aquino, “Relativistic Aspects of Nuclear Physics” (World Scientific 1990) pp. 271-307.
M. Moshinsky, G. Loyola, C. Villegas, Notas de Física. Proceedings of XIII Oaxtepec Conference on Nuclear Physics 1990, pp. 187-196.
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© 1993 Springer Science+Business Media New York
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Moshinsky, M. (1993). The One Body Dirac Oscillator. In: Gruber, B. (eds) Symmetries in Science VI. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1219-0_42
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DOI: https://doi.org/10.1007/978-1-4899-1219-0_42
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