Sur la quantification d'un système mécanique avec des contraintes de deuxième classe
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 28 (1978) no. 2, pp. 207-223.
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     title = {Sur la quantification d'un syst\`eme m\'ecanique avec des contraintes de deuxi\`eme classe},
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Todorov, I. T. Sur la quantification d'un système mécanique avec des contraintes de deuxième classe. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 28 (1978) no. 2, pp. 207-223. http://www.numdam.org/item/AIHPA_1978__28_2_207_0/

[1] P.A.M. Dirac, Lectures on Quantum Mechanics (Belfer Graduate School of Science, Yeshiva University, N. Y., 1964).

[2] A.J. Hanson, T. Regge and C. Teitelboim, Constraint Hamiltonian Systems, Institute for Advanced Study, Princeton, preprint 10-74 (1975) et Academia Nazionale dei Lincei, Roma, 1976.

[3] V. Bargmann and I.T. Todorov, Spaces of analytic functions on a complex cone as carriers for the symmetric tensor representations of SO(n), J. Math. Phys., t. 18, 1977, p. 1141. | MR | Zbl

[4] H. Bacry, The de Sitter group L4,1 and the bound states of hydrogen atom, Nuovo Cimento, t. A 41, 1966, p. 222. H. Bacry, H. Ruegg and J.M. Souriau, Dynamical groups and spherical potentials in classical mechanics, Commun. Math. Phys., t. 3, 1966, p. 323.

[5] G. Györgyi, Kepler's equation, Fock variables, Bacry's generators and Dirac brackets, Nuovo Cimento, t. 53, 1968, p. 717. G. Györgyi, Integration of the dynamical symmetry group for the - 1/r potential, Acta Phys. Acad. Sci. Hungaricae, t. 27, 1969, p. 435.

[6] Convegno di Geometria Simplettica e Fisica Matematica, Rome, 1973. v. en particulier, les articles : B. Kostant, Symplectic spinors; D.J. Simms, Geometric quantization of the energy levels in the Kepler problem ; J.M. Souriau, Sur la variété de Kepler ; J. Elhadad, Sur l'interprétation en géométrie symplectique des états quantiques de l'atome d'hydrogène.

[7] E. Onofri and M. Pauri, Dynamical quantization, J. Math. Phys., t. 13, 1972, p. 533. | MR

[8] E. Onofri, Dynamical quantization of the Kepler manifold, Università di Parma, preprint IFPR-T-047, 1975. | MR

[9] E. Onofri, V. Fock, 40 years later, Lecture given at the Conference on Differential Geometric Methods in Mathematical Physics, University of Bonn, July, 1975.

[10] I.T. Todorov, Quasipotential approach to the two-body problem in quantum field theory. In: Properties of Fundamental Interactions, vol. 9, Part C, ed. A. Zichichi (Editrice Compositori, Bologna, 1973); v. aussi Phys. Rev., t. D 3, 1971, p. 2351. V.A. Rizov, I.T. Todorov and B.L. Aneva, Quasipotential approach for the Coulomb bound state problem for spin 0 and spin 1/2 particles, Nuclear Physics, t. B 98, 1975, p. 447. 2

[11] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Commun. Pure Appl. Math., t. 14, 1961, p. 187 and t. 20, 1967, p. 1. | MR | Zbl

[12] T.D. Newton and E.P. Wigner, Localized states for elementary systems, Rev. Mod. Phys., t. 21, 1949, p. 400. A.S. Wightman, On the localizability of quantum mechanical systems, Rev. Mod. Phys., t. 34, 1962, p. 845. | Zbl

[13] D.G. Currie and T.F. Jordan, Interactions in relativistic classical particle mechanics. In : Lectures in Theoretical Physics, vol. XA Quantum Theory and Statistical Physics, Ed. by A. O. Barut and W. E. Brittin (Gordon and Breach, N. Y., 1968), p. 91-139.

[14] G. Mack and I.T. Todorov, Irreducibility of the ladder representations of U(2,2) when restricted to the Poincaré subgroup, J. Math. Phys., t. 10, 1969, p. 2078. | MR | Zbl

[15] S.P. Alliluev, ZhETF, t. 33, 1957, p. 200 (English Translation : JETP, t. 6, 1958, p. 156). | Zbl

[16] M. Bander and C. Itzykson, Group theory and the hydrogen atom I, Rev. Mod. Phys., t. 38, 1966, p. 330. | MR

[17] E.B. Aranson, I.A. Malkin and V.I. Manko, Dynamical symmetries in quantum theory, Sov. J. Particles Nucl., t. 5, 1974, p. 47 (p. 122 dans l'édition russe). | MR

[18] H.H. Rogers, Symmetry properties of the classical Kepler problem, J. Math. Phys., t. 14, 1973, p. 1125. | Zbl