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Geometry of real and complex canonical transformations in quantum mechanics

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Group Theoretical Methods in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 79))

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References

  1. J. AGUILAR and J.M. COMBES Comm. math. Phys. 22, 269–279 (1971).

    Google Scholar 

  2. R.F.V. ANDERSON J. Funct. An. 4, 240–269 (1969).

    Google Scholar 

  3. J. Funct. An. 6, 110–115 (1970).

    Google Scholar 

  4. J. Funct. An. 9 (1972).

    Google Scholar 

  5. J.P. ANTOINE and A. GROSSMANN J. Funct. An. 23, 369–378 (1976).

    Google Scholar 

  6. J. Funct. An. 23, 379–391 (1976).

    Google Scholar 

  7. V.I. ARNOLD Functional Analysis and Applications (russian) 1, 1 (1967).

    Google Scholar 

  8. N. ARONSZAJN Trans. Am. Math. Soc. 68, 337–404 (1950).

    Google Scholar 

  9. E. ARTIN Geometric algebra, Interscience 1957.

    Google Scholar 

  10. D. BABBIT Certain Hilbert spaces of analytic functions associated with the Heisenberg group, Studies in Mathematical Physics (Essays in honor of V. Bargmann, ed. E.H. Lieb, B. Simon, A.S. Wightman), Princeton Univ. Press 1976, page 19.

    Google Scholar 

  11. D. BABBIT and E. BALSLEV J. Funct. An. 18, 1 (1975).

    Google Scholar 

  12. G.A. BAKER Phys. Rev. 109, 2198 (1958).

    Google Scholar 

  13. E. BALSLEV Comm. math. Phys. 52, 127 (1977).

    Google Scholar 

  14. D. BABBIT and E. BALSLEV Comm. math. Phys. 35, 173–179 (1974).

    Google Scholar 

  15. E. BALSLEV and J.M. COMBES Comm. math. Phys. 22, 280–299 (1971).

    Google Scholar 

  16. V. BARGMANN Comm. Pure and Appl. Math. 14, 187–214 (1961).

    Google Scholar 

  17. V. BARGMANN Comm. Pure and Appl. Math. 20, 1–101 (1967).

    Google Scholar 

  18. V. BARGMANN Group representations in Hilbert spaces of analytic functions (Analytic Methods in Physics, R. Newton Ed.) pp. 27–63.

    Google Scholar 

  19. F.A. BEREZIN Comm. math. Phys. 40, 153 (1975).

    Google Scholar 

  20. F.A. BEREZIN Mat. Sbornik 86, (128) (1971) No4. Math. USSR Sbornik Vol. 1J (1971) No4.

    Google Scholar 

  21. F.A. BEREZIN and M.A. SUBIN Symbols of Operators and Quantization (Colloquia Mathematica Societatis Janos Boylai, 5; Hilbert space operators, B. Sz Nagy ed. Tihany, Hungary 1970)/

    Google Scholar 

  22. P. BERNAT, N. CONZE, M. DUFLO, M. LEVY-NAHAS, M. RAIS, P. RENOUARD, M. VERGNE Representations de groupes de Lie résolubles, Mém. Soc. Math. France 4, (1972).

    Google Scholar 

  23. R.J. BLATTNER Quantization and representation theory, Proc. Symp. Pure Math. Vol. 26, Am. Math. Soc. Providence R.I. (1974).

    Google Scholar 

  24. R.J. BLATTNER The metalinear geometry of non-real polarizations Conference on Differential Geometrical Methods in Mathematical Physics Universität Bonn, 1–4 July 1975 (Lecture Notes in Math., Vol.570).

    Google Scholar 

  25. M. BRUNET and P. KRAMER Complex extension of the representation of the symplectic group associated with the canonical commutation relations, Preprint University of Tübingen.

    Google Scholar 

  26. G. BURDET, M. PERRIN, M. PERROUD Generating functions for the affine symplectic group, Preprint U.of Montreal.

    Google Scholar 

  27. J.M. COMBES and L. THOMAS Comm. math. Phys. 34, 251–270 (1970).

    Google Scholar 

  28. R. CRESSMAN J. Funct. An. 22, 405 (1976).

    Google Scholar 

  29. I. DAUBECHIES and A. GROSSMANN in preparation.

    Google Scholar 

  30. U. Fano Rev. Mod. Phys. 29, 74

    Google Scholar 

  31. A. GROSSMANN Comm. math. Phys. 48, 191 (1976).

    Google Scholar 

  32. A. GROSSMANN and P. HUGUENIN in preparation.

    Google Scholar 

  33. A. GROSSMANN, G. LOUPIAS and E.M. STEIN Ann. Inst. Fourier 18, 343 (1968).

    Google Scholar 

  34. P. HUGUENIN Zeitsch. für Naturf. 28a, 1090 (1968).

    Google Scholar 

  35. P. IMRE, E. OZIZMIR, M. ROSENBAUM, P.F. ZWEIFEL Journ. Math. Phys. 8 1097

    Google Scholar 

  36. C. ITZYKSON Comm. math. Phys. 4, 92

    Google Scholar 

  37. D. KASTLER Comm. math. Phys. 1, 14–48 (1965). Lecture Notes (Argonne Nat. Lab).

    Google Scholar 

  38. P. KRAMER, M. MOSHINSKY and T.H. SELIGMAN Complex extensions of canonical transformations and quantum mechanics, in Loebl, Ed: Group Theory and its applications, vol. III (1975).

    Google Scholar 

  39. P. KRAMER and D. SCHENZLE Revista Mexicana de Fisica, 22, 25 (1973).

    Google Scholar 

  40. P. KRAMER Composite particles and symplectic (semi) groups, Proc. VI Int. Coll. Group theoretical methods in physics, Tübingen 1977.

    Google Scholar 

  41. H.A. KRAMERS Quantum mechanics (North-Holland) 1964, pp. 157–158.

    Google Scholar 

  42. J.G. KRUGER and A. POFFYN Physica 77A

    Google Scholar 

  43. R.B. LAVINE The Weyl transform: Fourier analysis of operators in L2-spaces, Ph.D. Thesis M.I.T. 1965.

    Google Scholar 

  44. J. LERAY Coll. Int. CNRS no 237 (Juin 1974) Aix-en-Provence, Géometrie symplectique et physique mathématique, edition du CNRS 1975, p. 237.

    Google Scholar 

  45. G. LOUPIAS and S. MIRACLE-SOLE Comm. math. Phys. 2, 31 (1966).

    Google Scholar 

  46. G. MACKEY in Functional analysis and related fields, F. Browder, ed., Springer 1970.

    Google Scholar 

  47. M. MOSHINSKY Canonical transformations and quantum mechanics, (Lectures and collection of papers) Escuola Latino-Americana de Fisica, 1974.

    Google Scholar 

  48. M. MOSHINSKY and M. QUESNE Journ. Math. Phys. 12 1772 (1971).

    Google Scholar 

  49. M. MOSHINSKY SIAM J. Appl. Math. 25, 193 (1973).

    Google Scholar 

  50. J.E. MOYAL Proc. Camb. Phil. Soc. 45, 299 (1949)

    Google Scholar 

  51. J.C. POOL J. Math. Phys. 7, 66 (1966).

    Google Scholar 

  52. E.T. POULSEN Quantization in Hamiltonian Particle dynamics Lecture notes in Mathematics 399, Springer, Berlin 1974.

    Google Scholar 

  53. E.A. REMLER Ann. Phys. 95, 455–495 (1975).

    Google Scholar 

  54. I. SATAKE Advances Math. 7, 83–110 (1971).

    Google Scholar 

  55. I.E. SEGAL Math. Scand. 13, 31–43 (1963).

    Google Scholar 

  56. I.E. SEGAL The complex-wave representation of the free boson field, M.I.T. Preprint.

    Google Scholar 

  57. B. SIMON Ann.Math. 97, 247–274 (1973).

    Google Scholar 

  58. S. STERNBERG Proc. VIth Int. Coll. Group Theoretical Methods in Physics, Tübingen, 1977.

    Google Scholar 

  59. V. GUILLEMIN and S. STERNBERG Geometric Asymptotics, A.M.S.

    Google Scholar 

  60. D. SHALE Trans. Am. Math. Soc. 103, 149 (1962).

    Google Scholar 

  61. J.M. SOURIAU Structure des Systèmes Dynamiques, Dunod 1970. Proceedings of the 4th Int. Coll. Group Theoretical Methods in Physics, Nijmegen, 1975, A. Janner et al., eds.

    Google Scholar 

  62. A. WEIL Acta Math. 111, 143 (1963).

    Google Scholar 

  63. H. WEYL Theory of Groups and Quantum Mechanics (English Translation, Dover 1950).

    Google Scholar 

  64. E. WINTER Phys. Rev. 40, 749 (1932).

    Google Scholar 

  65. R.J. GLAUBER Phys. Rev. 131, 2766 (1963).

    Google Scholar 

  66. J.R. KLAUDER J. Math. Phys. 11, 609 (1970).

    Google Scholar 

  67. C. van WINTER J. Math. An. Appl. 47, 633-48, 368 (1974).

    Google Scholar 

  68. B. KOSTANT Lecture Notes in Math. Vol. 170, Springer Verlag, Berlin 1970, pp. 237–253.

    Google Scholar 

  69. B. KOSTANT, Symposia Math. Vol. XIV, Academic Press, London 1974, pp. 139–152.

    Google Scholar 

  70. A. VOROS An Algebra of Pseudodifferential Operators and Asymptotics of Quantum Mechanics, Preprint, submitted to Journ. Funct. Anal.

    Google Scholar 

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  1. Centre de Physique Théorique C.N.R.S., Marseille

    A. Grossmann

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  1. A. Grossmann
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P. Kramer A. Rieckers

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© 1978 Springer-Verlag

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Grossmann, A. (1978). Geometry of real and complex canonical transformations in quantum mechanics. In: Kramer, P., Rieckers, A. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08848-2_9

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  • DOI: https://doi.org/10.1007/3-540-08848-2_9

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