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Fourier-like kernels in geometric quantization

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Rozprawy Matematyczne tom/nr w serii: 128 wydano: 1976
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CONTENTS
I. Introduction............................................................................................................................................... 5
II. Preliminary notions................................................................................................................................ 7
III. Geometric quantization.........................................................................................................................12
   A. Elements of symplectic geometry................................................................12
   B. Quantum bundles...........................................................................................13
   C. Polarizations....................................................................................................16
   D. Hilbert space connected with a polarized symplectic manifold............ 18
   E. Kostant quantization of physical quantities............................................... 28
IV. Kernel quantization............................................................................................................................... 41
   A. Geometric quantization of canonical diffeomorphisms.......................... 41
   B. Distinguished kernels................................................................................... 43
   C. Kernel representation of quantized operators.......................................... 67
References.................................................................................................................................................. 78
Słowa kluczowe
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Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 128
Liczba stron
79
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Opis fizyczny
Dissertationes Mathematicae, Tom CXXVIII
Daty
wydano
1976
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autor
Bibliografia
  • [1] R. Abraham Foundations of mechanics, Benjamin, New York 1967.
  • [2] L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), p. 255-354.
  • [3] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), p. 187-214.
  • [4] R. Blattner, Quantization and representation theory, in Proceedings of A.M.S. 1972 Summer Institute on Group Representations.
  • [5] L. Hörmander, Fourier integral operators, I, Acta Math. 127 (1971), p. 79-183.
  • [6] B. Kostant, Quantization and unitary representations. Lecture Notes in Mathematics, 170, Springer, Berlin 1970, p. 87.
  • [7] B. Kostant, Symplectic spinors, in Geometria Simplettica e Fisica Mathematica, Symposia Math. 14, Academic Press., London, New York 1974, p. 138-152.
  • [8] H. Meschkowski, Hilbertsche Räume mit Kernfunktion, Berlin 1962.
  • [9] R. S. Palais, A global formulation of the Lie theory of transportation groups, Memoirs of A.M.S. 22, 1955.
  • [10] A. M. Perelomov, Coherent states for arbitrary Lie group, Commun. Math. Phys. 26 (1972), p. 222-236.
  • [11] P. Renouard, Variétés symplectiques et quantification, Thèse, Orsay 1969.
  • [12] D. J. Simms, Geometric quantization of energy levels in the Kepler problem, in Geometria Simplettica e Fisica Matematica, INDAM Rome 1973, Symposia Math. 14, Academic Press., London, New York 1974, p. 138-152.
  • [13] J. M. Souriau, Structures des systèmes dynamiques, Paris 1970.
  • [14] A. Weil, Varietés kahleriennes, Actualités Scientifiques et Industrielles 1267, Paris 1958.
  • [15] F. A. Berezin, Quantization in complex bounded domains, English translation: Soviet Math. Dokl. 14 (1973), p. 1209-1513.
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