no. 6
On the classical and quantum evolution of lagrangian half-forms in phase space
Annales de l'I.H.P. Physique théorique, Tome 70 (1999) no. 6, pp. 547-573 
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     author = {De Gosson, Maurice},
     title = {On the classical and quantum evolution of lagrangian half-forms in phase space},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {547--573},
     year = {1999},
     publisher = {Gauthier-Villars},
     volume = {70},
     number = {6},
     mrnumber = {1693584},
     zbl = {1049.53055},
     language = {en},
     url = {https://www.numdam.org/item/AIHPA_1999__70_6_547_0/}
}
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De Gosson, Maurice. On the classical and quantum evolution of lagrangian half-forms in phase space. Annales de l'I.H.P. Physique théorique, Tome 70 (1999) no. 6, pp. 547-573. https://www.numdam.org/item/AIHPA_1999__70_6_547_0/

[1] V.I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed., Graduate Texts in Mathematics, Springer, Berlin, New York, 1989. | MR

[2] S.E. Cappell, R. Lee and E.Y. Miller, On the Maslov index, Comm. Pure Appl. Math. 47 (1994) 121-180. | Zbl | MR

[3] D. Bohm and B.J. Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory, Routledge, London and New York, 1993. | Zbl | MR

[4] P. Dazord, Invariants homotopiques attachés aux fibrés symplectiques, Ann. Inst. Fourier, Grenoble 29 (2) (1979) 25-78. | Zbl | MR | Numdam

[5] M. Demazure, Classe de Maslov II, Exposé No. 10, in: Séminaire sur le Fibré Cotangent, Orsay 1975-1976.

[6] G.B. Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 1989. | Zbl | MR

[7] M. De Gosson, La définition de l'indice de Maslov sans hypothèse de transversalité, C. R. Acad. Sci. Paris Série I 309 (1990) 279-281. | Zbl

[8] M. De Gosson, La relation entre Sp∞, revêtement universel du groupe symplectique Sp et Sp x Z, C. R. Acad. Sci. Paris 310 (1990) 245-248. | Zbl | MR

[9] M. De Gosson, Maslov indices on the metaplectic group Mp(n), Ann. Inst. Fourier, Grenoble 40 (3) (1990) 537-555. | Zbl | MR | Numdam

[10] M. De Gosson, The structure of q-symplectic geometry, J. Math. Pures Appl. 71 (1992) 429-453. | Zbl | MR

[11] M. De Gosson, Cocycles de Demazure-Kashiwara et géométrie métaplectique, J. Geom. Phys. 9 (1992) 255-280. | Zbl | MR

[12] M. De Gosson, On the Leray-Maslov quantization of Lagrangian manifolds, J. Geom. Phys. 13 (1994) 158-168. | Zbl | MR

[13] M. De Gosson, Maslov Classes, Metaplectic Representation and Lagrangian Quantization, Research Notes in Mathematics, Vol. 95, Akademie-Verlag, Berlin, 1996. | Zbl

[14] M. De Gosson, On half-form quantization of Lagrangian manifolds, Bull. Sci. Math. 1997.

[15] V. Guillemin and S. Sternberg, Geometric Asymptotics, Math. Surveys Monographs, Vol. 14, Amer. Math. Soc., Providence, RI, 1977. | MR

[16] V. Guillemin and S. Sternberg, Symplectic Techniques in Physics, Cambridge University Press, Cambridge, MA, 1984. | Zbl | MR

[17] P.R. Holland, The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics, Cambridge University Press, Cambridge, MA, 1993. | Zbl | MR

[18] J. Leray, Lagrangian Analysis, MIT Press, Cambridge, MA, London, 1981; Analyse Lagamgienne RCP 25, Strasbourg 1978; Collège de France, 1976-1977. | MR

[19] J. Leray, The meaning of Maslov's asymptotic method the need of Planck's constant in mathematics, Bull. Amer. Math. Soc., Symposium on the Mathematical Heritage of Henri Poincaré, 1980. | Zbl

[20] G. Lion and M. Vergne, The Weil Representation, Maslov Index and Theta Series, Progress in Math., Birkhäuser, Boston, 1980. | Zbl | MR

[21] V.P. Maslov, Théorie des Perturbations et Méthodes Asymptotiques, Dunod, Paris, 1972; Perturbation Theory and Asymptotic Methods, Moscow, MGU, 1965 (in Russian).

[22] V.P. Maslov and M.V. Fedoriuk, Semi-Classical Approximations in Quantum Mechanics, Reidel, Boston, 1981.

[23] A.S. Mischenko, V.E. Shatalov and B. Yu. Sternin, Lagrangian Manifolds and the Maslov Canonical Operator, Springer, Berlin, 1990. | Zbl

[24] J.M. Souriau, Indice de Maslov des variétés Lagrangiennes orientables, C. R. Acad. Sci. Paris Série A 276 (1973) 1025-1026. | Zbl | MR