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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G.W. Mackey, Quantum mechanics and induced representations, Benjamin, New York 1968
V.S. Varadarajan, Geometry of quantum theory Vols. I,II, Van Nostrand, Princeton 1968
H.D. Doebner, J. Tolar, Quantum mechanics on homogeneous spaces, J.Math.Phys. 16, 1975, pp 975–984
S.K. Berberian, Notes on spectral theory, Van Nostrand, Princeton 1966
S.T. Ali, G.G. Emch, Fuzzy observables in quantum mechanics, J.Math.Phys. 15, 1974, 176–182
A.S. Wightman, On the localizability of quantum mechanical systems, Rev.Mod.Phys. 34, 1962, 845–872
M. Reed, B. Simon, Methods of modern mathematical physics, Vol.I, Academic Press, New York 1972
P.R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, Chelsea Publ.Comp., New York 1957
J. Dieudonné, Foundations of modern analysis, Academic Press, New York 1960
B. Angermann, Über Quantisierungen lokalisierter Systeme-Physikalisch interpretierbare mathematische Modelle, Ph.D.Thesis, Clausthal 1983
J.V. Neumann, Die Eindeutigkeit der Schrödinger'schen Operatoren, Math.Ann. 104, 1931, 570–578
B. Angermann, H.D. Doebner, Homotopy groups and the quantization of localizable systems, Physica 114A, 1982, 433–439
H.D. Doebner, J. Tolar, On global properties of quantum systems, in: Symmetries in science, Plenum Press, New York 1980
I.E. Segal, Quantization of non-linear systems, J.Math.Phys. 1, 1960, 468–488
D.W. Kahn, Introduction to global analysis, Academic Press, New York 1980
N. Dunford, J.T. Schwartz, Linear operators, Vol.II, Interscience, New York 1957
R.S. Palais, Logarithmically exact differential forms, Proc.Amer.Math.Soc. 12, 1961, 50–52
S. Kobayashi, K. Nomizu, Foundations of differential geometry, Vol.I, Interscience-Wiley, New York 1963
G. Birkhoff, Lattice theory, Amer.Math.Soc.Publ. XXV, 1967
G. Birkhoff, J.V. Neumann, On the logic of quantum mechanics, Ann. of Math. 37, 1936, 823–843
J.M. Jauch, Foundations of quantum mechanics, Addison Wesley, London 1973
P.R. Halmos, Measure theory, Van Nostrand, Princeton 1968
B. Kostant, Quantization and unitary representations, Springer Lecture Notes in Mathematics 170, 1970, 86–208
R.O. Wells, Differential analysis on complex manifolds, Springer, New York 1973.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0073173
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12710-9
Online ISBN: 978-3-540-38695-7
eBook Packages: Springer Book Archive
