On the classical and quantum evolution of lagrangian half-forms in phase space

Maurice De Gosson

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 70, Issue: 6, page 547-573
  • ISSN: 0246-0211

How to cite

top

De Gosson, Maurice. "On the classical and quantum evolution of lagrangian half-forms in phase space." Annales de l'I.H.P. Physique théorique 70.6 (1999): 547-573. <http://eudml.org/doc/76830>.

@article{DeGosson1999,
author = {De Gosson, Maurice},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {half-forms; Maslov's class; Bohmian},
language = {eng},
number = {6},
pages = {547-573},
publisher = {Gauthier-Villars},
title = {On the classical and quantum evolution of lagrangian half-forms in phase space},
url = {http://eudml.org/doc/76830},
volume = {70},
year = {1999},
}

TY - JOUR
AU - De Gosson, Maurice
TI - On the classical and quantum evolution of lagrangian half-forms in phase space
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 70
IS - 6
SP - 547
EP - 573
LA - eng
KW - half-forms; Maslov's class; Bohmian
UR - http://eudml.org/doc/76830
ER -

References

top
  1. [1] V.I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed., Graduate Texts in Mathematics, Springer, Berlin, New York, 1989. MR997295
  2. [2] S.E. Cappell, R. Lee and E.Y. Miller, On the Maslov index, Comm. Pure Appl. Math.47 (1994) 121-180. Zbl0805.58022MR1263126
  3. [3] D. Bohm and B.J. Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory, Routledge, London and New York, 1993. Zbl0990.81503MR1326828
  4. [4] P. Dazord, Invariants homotopiques attachés aux fibrés symplectiques, Ann. Inst. Fourier, Grenoble29 (2) (1979) 25-78. Zbl0378.58011MR539693
  5. [5] M. Demazure, Classe de Maslov II, Exposé No. 10, in: Séminaire sur le Fibré Cotangent, Orsay1975-1976. 
  6. [6] G.B. Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 1989. Zbl0682.43001MR983366
  7. [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. Zbl0705.22012
  8. [8] M. De Gosson, La relation entre Sp∞, revêtement universel du groupe symplectique Sp et Sp x Z, C. R. Acad. Sci. Paris310 (1990) 245-248. Zbl0732.22001MR1042855
  9. [9] M. De Gosson, Maslov indices on the metaplectic group Mp(n), Ann. Inst. Fourier, Grenoble40 (3) (1990) 537-555. Zbl0705.22013MR1091832
  10. [10] M. De Gosson, The structure of q-symplectic geometry, J. Math. Pures Appl.71 (1992) 429-453. Zbl0829.58015MR1191584
  11. [11] M. De Gosson, Cocycles de Demazure-Kashiwara et géométrie métaplectique, J. Geom. Phys.9 (1992) 255-280. Zbl0776.53022MR1171138
  12. [12] M. De Gosson, On the Leray-Maslov quantization of Lagrangian manifolds, J. Geom. Phys.13 (1994) 158-168. Zbl0795.58022MR1260596
  13. [13] M. De Gosson, Maslov Classes, Metaplectic Representation and Lagrangian Quantization, Research Notes in Mathematics, Vol. 95, Akademie-Verlag, Berlin, 1996. Zbl0872.58031
  14. [14] M. De Gosson, On half-form quantization of Lagrangian manifolds, Bull. Sci. Math.1997. Zbl0878.58023
  15. [15] V. Guillemin and S. Sternberg, Geometric Asymptotics, Math. Surveys Monographs, Vol. 14, Amer. Math. Soc., Providence, RI, 1977. MR516965
  16. [16] V. Guillemin and S. Sternberg, Symplectic Techniques in Physics, Cambridge University Press, Cambridge, MA, 1984. Zbl0576.58012MR770935
  17. [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. Zbl0854.00009MR1341368
  18. [18] J. Leray, Lagrangian Analysis, MIT Press, Cambridge, MA, London, 1981; Analyse Lagamgienne RCP25, Strasbourg1978; Collège de France, 1976-1977. MR644633
  19. [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. Zbl0532.35068
  20. [20] G. Lion and M. Vergne, The Weil Representation, Maslov Index and Theta Series, Progress in Math., Birkhäuser, Boston, 1980. Zbl0444.22005MR573448
  21. [21] V.P. Maslov, Théorie des Perturbations et Méthodes Asymptotiques, Dunod, Paris, 1972; Perturbation Theory and Asymptotic Methods, Moscow, MGU, 1965 (in Russian). Zbl0653.35002
  22. [22] V.P. Maslov and M.V. Fedoriuk, Semi-Classical Approximations in Quantum Mechanics, Reidel, Boston, 1981. 
  23. [23] A.S. Mischenko, V.E. Shatalov and B. Yu. Sternin, Lagrangian Manifolds and the Maslov Canonical Operator, Springer, Berlin, 1990. Zbl0727.58001
  24. [24] J.M. Souriau, Indice de Maslov des variétés Lagrangiennes orientables, C. R. Acad. Sci. Paris SérieA276 (1973) 1025-1026. Zbl0254.58007MR319227

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.