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Quantum kinematics on smooth manifolds

  • B. Angermann
  • H. D. Doebner
  • J. Tolar
Part II Quantization Procedures
Part of the Lecture Notes in Mathematics book series (LNM, volume 1037)

Keywords

Line Bundle Borel Measure Momentum Operator Separable Hilbert Space Selfadjoint Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    G.W. Mackey, Quantum mechanics and induced representations, Benjamin, New York 1968zbMATHGoogle Scholar
  2. [2]
    V.S. Varadarajan, Geometry of quantum theory Vols. I,II, Van Nostrand, Princeton 1968Google Scholar
  3. [3]
    H.D. Doebner, J. Tolar, Quantum mechanics on homogeneous spaces, J.Math.Phys. 16, 1975, pp 975–984MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    S.K. Berberian, Notes on spectral theory, Van Nostrand, Princeton 1966zbMATHGoogle Scholar
  5. [5]
    S.T. Ali, G.G. Emch, Fuzzy observables in quantum mechanics, J.Math.Phys. 15, 1974, 176–182MathSciNetCrossRefGoogle Scholar
  6. [6]
    A.S. Wightman, On the localizability of quantum mechanical systems, Rev.Mod.Phys. 34, 1962, 845–872MathSciNetCrossRefGoogle Scholar
  7. [7]
    M. Reed, B. Simon, Methods of modern mathematical physics, Vol.I, Academic Press, New York 1972Google Scholar
  8. [8]
    P.R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, Chelsea Publ.Comp., New York 1957zbMATHGoogle Scholar
  9. [9]
    J. Dieudonné, Foundations of modern analysis, Academic Press, New York 1960zbMATHGoogle Scholar
  10. [10]
    B. Angermann, Über Quantisierungen lokalisierter Systeme-Physikalisch interpretierbare mathematische Modelle, Ph.D.Thesis, Clausthal 1983Google Scholar
  11. [11]
    J.V. Neumann, Die Eindeutigkeit der Schrödinger'schen Operatoren, Math.Ann. 104, 1931, 570–578MathSciNetCrossRefGoogle Scholar
  12. [12]
    B. Angermann, H.D. Doebner, Homotopy groups and the quantization of localizable systems, Physica 114A, 1982, 433–439MathSciNetGoogle Scholar
  13. [13]
    H.D. Doebner, J. Tolar, On global properties of quantum systems, in: Symmetries in science, Plenum Press, New York 1980Google Scholar
  14. [14]
    I.E. Segal, Quantization of non-linear systems, J.Math.Phys. 1, 1960, 468–488zbMATHCrossRefGoogle Scholar
  15. [15]
    D.W. Kahn, Introduction to global analysis, Academic Press, New York 1980zbMATHGoogle Scholar
  16. [16]
    N. Dunford, J.T. Schwartz, Linear operators, Vol.II, Interscience, New York 1957Google Scholar
  17. [17]
    R.S. Palais, Logarithmically exact differential forms, Proc.Amer.Math.Soc. 12, 1961, 50–52MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    S. Kobayashi, K. Nomizu, Foundations of differential geometry, Vol.I, Interscience-Wiley, New York 1963Google Scholar
  19. [19]
    G. Birkhoff, Lattice theory, Amer.Math.Soc.Publ. XXV, 1967Google Scholar
  20. [20]
    G. Birkhoff, J.V. Neumann, On the logic of quantum mechanics, Ann. of Math. 37, 1936, 823–843MathSciNetCrossRefGoogle Scholar
  21. [21]
    J.M. Jauch, Foundations of quantum mechanics, Addison Wesley, London 1973Google Scholar
  22. [22]
    P.R. Halmos, Measure theory, Van Nostrand, Princeton 1968Google Scholar
  23. [23]
    B. Kostant, Quantization and unitary representations, Springer Lecture Notes in Mathematics 170, 1970, 86–208MathSciNetGoogle Scholar
  24. [24]
    R.O. Wells, Differential analysis on complex manifolds, Springer, New York 1973.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • B. Angermann
    • 1
  • H. D. Doebner
    • 1
  • J. Tolar
    • 2
  1. 1.Institute for Theoretical Physics ATechnical University of ClausthalClausthalGermany F.R.
  2. 2.Faculty of Nuclear Science and Physical EngineeringCzech Technical UniversityPragueCzechoslovakia

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