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Geometric quantization of presymplectic manifolds. (English) Zbl 0521.58035

MSC:
53D50Geometric quantization
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
53C80Applications of global differential geometry to physics
References:
[1]Abraham, R., Marsden, J. E.: Foundations of Mechanics, 2nd Ed. Reading, Mass.: Benjamin/Cummings Publ. Comp. 1978.
[2]Aldaya, V., de Azc?rraga, J. A.: Quantization as a consequence of the symmetry group: An approach to geometric quantization. J. Math. Phys.23, 1297-1305 (1982). · Zbl 0502.58018 · doi:10.1063/1.525513
[3]de Barros, C. M.: Sur la g?ometrie diff?rentielle des formes diff?rentielles ext?rieures quadratiques. In: Atti Convegno Intern. Geometria Differenziale, Bologna 1967, pp. 117-142. Bologna: Ed. Zanichelli. 1967.
[4]Gotay, M. J.: On coisotropic imbeddings of presymplectic manifolds. Preprint. Univ. Calgary. 1980.
[5]Gotay, M. J., ?niatycki, J.: On the quantization of presymplectic dynamical systems via coisotropic imbeddings. Comm. Math. Phys.82, 377-389 (1981). · Zbl 0508.58024 · doi:10.1007/BF01237045
[6]G?nther, C.: Presymplectic manifolds and the quantization of relativistic particle systems. In: Differential Geometrical Methods in Mathematical Physics, Proc. Conf. Salamanca 1979, pp. 383-400. Lecture Notes Math. 836. Berlin-Heidelberg-New York: Springer. 1980.
[7]Lichnerowicz, A.: Les vari?t?s de Poisson et leurs alg?bres de Lie associ?es. J. Diff. Geom.12, 253-300 (1977).
[8]Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds. T?hoku Math. J.10, 338-345 (1958). · Zbl 0086.15003 · doi:10.2748/tmj/1178244668
[9]Satake, I.: The Gauss-Bonnet theorem forV-manifolds. J. Math. Soc. Japan9, 464-492 (1957). · Zbl 0080.37403 · doi:10.2969/jmsj/00940464
[10]?niatycki, J.: Geometric Quantization and Quantum Mechanics. Berlin-Heidelberg-New York: Springer. 1980.
[11]?niatycki, J.: Constraints and Quantization. Preprint. Univ. Calgary. 1982.
[12]Souriau, J. M.: Structures des Syst?mes Dynamiques. Paris: Dunod. 1970.
[13]Vaisman, I.: Cohomology and Differential Forms. New York-Basel: M. Dekker. 1973.
[14]Vaisman, I.: Basic ideas of geometric quantization. Rend. Sem. Mat. Torino37, 31-41 (1979).
[15]Vaisman, I.: A coordinatewise formulation of geometric quantization. Ann. Inst. H. Poincar?31, 5-24 (1979).
[16]Woodhouse, N.: Geometric Quantization. Oxford: Clarendon, Press. 1980.
[17]Yano, K.: The Theory of Lie Derivatives and its Applications. Amsterdam: North Holland. 1957.