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Quantum kinematics on smooth manifolds

  • Part II Quantization Procedures
  • Conference paper
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Non-linear Partial Differential Operators and Quantization Procedures

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1037))

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References

  1. G.W. Mackey, Quantum mechanics and induced representations, Benjamin, New York 1968

    MATH  Google Scholar 

  2. V.S. Varadarajan, Geometry of quantum theory Vols. I,II, Van Nostrand, Princeton 1968

    Google Scholar 

  3. H.D. Doebner, J. Tolar, Quantum mechanics on homogeneous spaces, J.Math.Phys. 16, 1975, pp 975–984

    Article  MathSciNet  MATH  Google Scholar 

  4. S.K. Berberian, Notes on spectral theory, Van Nostrand, Princeton 1966

    MATH  Google Scholar 

  5. S.T. Ali, G.G. Emch, Fuzzy observables in quantum mechanics, J.Math.Phys. 15, 1974, 176–182

    Article  MathSciNet  Google Scholar 

  6. A.S. Wightman, On the localizability of quantum mechanical systems, Rev.Mod.Phys. 34, 1962, 845–872

    Article  MathSciNet  Google Scholar 

  7. M. Reed, B. Simon, Methods of modern mathematical physics, Vol.I, Academic Press, New York 1972

    Google Scholar 

  8. P.R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, Chelsea Publ.Comp., New York 1957

    MATH  Google Scholar 

  9. J. Dieudonné, Foundations of modern analysis, Academic Press, New York 1960

    MATH  Google Scholar 

  10. B. Angermann, Über Quantisierungen lokalisierter Systeme-Physikalisch interpretierbare mathematische Modelle, Ph.D.Thesis, Clausthal 1983

    Google Scholar 

  11. J.V. Neumann, Die Eindeutigkeit der Schrödinger'schen Operatoren, Math.Ann. 104, 1931, 570–578

    Article  MathSciNet  Google Scholar 

  12. B. Angermann, H.D. Doebner, Homotopy groups and the quantization of localizable systems, Physica 114A, 1982, 433–439

    MathSciNet  Google Scholar 

  13. H.D. Doebner, J. Tolar, On global properties of quantum systems, in: Symmetries in science, Plenum Press, New York 1980

    Google Scholar 

  14. I.E. Segal, Quantization of non-linear systems, J.Math.Phys. 1, 1960, 468–488

    Article  MATH  Google Scholar 

  15. D.W. Kahn, Introduction to global analysis, Academic Press, New York 1980

    MATH  Google Scholar 

  16. N. Dunford, J.T. Schwartz, Linear operators, Vol.II, Interscience, New York 1957

    Google Scholar 

  17. R.S. Palais, Logarithmically exact differential forms, Proc.Amer.Math.Soc. 12, 1961, 50–52

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Kobayashi, K. Nomizu, Foundations of differential geometry, Vol.I, Interscience-Wiley, New York 1963

    Google Scholar 

  19. G. Birkhoff, Lattice theory, Amer.Math.Soc.Publ. XXV, 1967

    Google Scholar 

  20. G. Birkhoff, J.V. Neumann, On the logic of quantum mechanics, Ann. of Math. 37, 1936, 823–843

    Article  MathSciNet  Google Scholar 

  21. J.M. Jauch, Foundations of quantum mechanics, Addison Wesley, London 1973

    Google Scholar 

  22. P.R. Halmos, Measure theory, Van Nostrand, Princeton 1968

    Google Scholar 

  23. B. Kostant, Quantization and unitary representations, Springer Lecture Notes in Mathematics 170, 1970, 86–208

    MathSciNet  Google Scholar 

  24. R.O. Wells, Differential analysis on complex manifolds, Springer, New York 1973.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Theoretical Physics A, Technical University of Clausthal, Clausthal, Germany F.R.

    B. Angermann & H. D. Doebner

  2. Faculty of Nuclear Science and Physical Engineering, Czech Technical University, Prague, Czechoslovakia

    J. Tolar

Authors
  1. B. Angermann
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  2. H. D. Doebner
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  3. J. Tolar
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Clausthal, 3392, Clausthal-Zellerfeld, Federal Republic of Germany

    Stig I. Andersson  & Heinz-Dietrich Doebner  & 

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© 1983 Springer-Verlag Berlin Heidelberg

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Angermann, B., Doebner, H.D., Tolar, J. (1983). Quantum kinematics on smooth manifolds. In: Andersson, S.I., Doebner, HD. (eds) Non-linear Partial Differential Operators and Quantization Procedures. Lecture Notes in Mathematics, vol 1037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073173

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  • DOI: https://doi.org/10.1007/BFb0073173

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12710-9

  • Online ISBN: 978-3-540-38695-7

  • eBook Packages: Springer Book Archive

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