@article{AIHPA_1999__70_6_547_0,
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},
volume = {71},
year = {1999},
pages = {547-573},
mrnumber = {1693584},
zbl = {1049.53055},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1999__70_6_547_0}
}
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 71 (1999) pp. 547-573. http://gdmltest.u-ga.fr/item/AIHPA_1999__70_6_547_0/
[1] , Mathematical Methods of Classical Mechanics, 2nd ed., Graduate Texts in Mathematics, Springer, Berlin, New York, 1989. | MR 997295
[2] , and , On the Maslov index, Comm. Pure Appl. Math. 47 (1994) 121-180. | MR 1263126 | Zbl 0805.58022
[3] and , The Undivided Universe: An Ontological Interpretation of Quantum Theory, Routledge, London and New York, 1993. | MR 1326828 | Zbl 0990.81503
[4] , Invariants homotopiques attachés aux fibrés symplectiques, Ann. Inst. Fourier, Grenoble 29 (2) (1979) 25-78. | Numdam | MR 539693 | Zbl 0378.58011
[5] , Classe de Maslov II, Exposé No. 10, in: Séminaire sur le Fibré Cotangent, Orsay 1975-1976.
[6] , Harmonic Analysis in Phase Space, Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 1989. | MR 983366 | Zbl 0682.43001
[7] , La définition de l'indice de Maslov sans hypothèse de transversalité, C. R. Acad. Sci. Paris Série I 309 (1990) 279-281. | Zbl 0705.22012
[8] , La relation entre Sp∞, revêtement universel du groupe symplectique Sp et Sp x Z, C. R. Acad. Sci. Paris 310 (1990) 245-248. | MR 1042855 | Zbl 0732.22001
[9] , Maslov indices on the metaplectic group Mp(n), Ann. Inst. Fourier, Grenoble 40 (3) (1990) 537-555. | Numdam | MR 1091832 | Zbl 0705.22013
[10] , The structure of q-symplectic geometry, J. Math. Pures Appl. 71 (1992) 429-453. | MR 1191584 | Zbl 0829.58015
[11] , Cocycles de Demazure-Kashiwara et géométrie métaplectique, J. Geom. Phys. 9 (1992) 255-280. | MR 1171138 | Zbl 0776.53022
[12] , On the Leray-Maslov quantization of Lagrangian manifolds, J. Geom. Phys. 13 (1994) 158-168. | MR 1260596 | Zbl 0795.58022
[13] , Maslov Classes, Metaplectic Representation and Lagrangian Quantization, Research Notes in Mathematics, Vol. 95, Akademie-Verlag, Berlin, 1996. | Zbl 0872.58031
[14] , On half-form quantization of Lagrangian manifolds, Bull. Sci. Math. 1997.
[15] and , Geometric Asymptotics, Math. Surveys Monographs, Vol. 14, Amer. Math. Soc., Providence, RI, 1977. | MR 516965
[16] and , Symplectic Techniques in Physics, Cambridge University Press, Cambridge, MA, 1984. | MR 770935 | Zbl 0576.58012
[17] , The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics, Cambridge University Press, Cambridge, MA, 1993. | MR 1341368 | Zbl 0854.00009
[18] , Lagrangian Analysis, MIT Press, Cambridge, MA, London, 1981; Analyse Lagamgienne RCP 25, Strasbourg 1978; Collège de France, 1976-1977. | MR 644633
[19] , 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 0532.35068
[20] and , The Weil Representation, Maslov Index and Theta Series, Progress in Math., Birkhäuser, Boston, 1980. | MR 573448 | Zbl 0444.22005
[21] , Théorie des Perturbations et Méthodes Asymptotiques, Dunod, Paris, 1972; Perturbation Theory and Asymptotic Methods, Moscow, MGU, 1965 (in Russian).
[22] and , Semi-Classical Approximations in Quantum Mechanics, Reidel, Boston, 1981.
[23] , and , Lagrangian Manifolds and the Maslov Canonical Operator, Springer, Berlin, 1990. | Zbl 0727.58001
[24] , Indice de Maslov des variétés Lagrangiennes orientables, C. R. Acad. Sci. Paris Série A 276 (1973) 1025-1026. | MR 319227 | Zbl 0254.58007