Vector Fields in Three-Space, Natural Internal Degrees of Freedom, Signal Transmission and Quantization

Results in Mathematics

Volumn 37, Issue 3-4, 2000, Pages 226-245

  Binz, Ernst ^a   Schempp, Walter ^b  

^a UNIVERSITY OF MANNHEIM   (Germany)

^b UNIVERSITY OF SIEGEN   (Germany)

Author keywords

Complex line bundles; quantization; Schr dinger representation; signal transmission

Indexed keywords

EID: 0001145026     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/BF03321995     Document Type: Article

References (17)

1. Berger M. and Gostiaux B., Differential Geometry: Manifolds, Curves, and Surfaces, GTM, Vol. 115, Springer-Verlag, New York, Berlin, Heidelberg 1988.
2. Binz E. and Schempp W., Quantum Teleportation and Spin Echo: A Unitary Symplectic Spinor Approach. In: Aspects of Complex Analysis, Differential Geometry, Mathematical Physics, and Applications, Dimiev S. and Sekigawa K. (Ed.), pp. 314–365, World Scientific, Singapore, New Jersey, London 1999.
3. Binz E. and Schempp W., Projective geometry and Keppler’s libration theory, Proc. Conference Goslar 1999 (in print).
4. Binz E. and Schempp W., Entanglement and Parataxy (to appear).
5. Binz E. and Schempp W., Quantum Systems: From Macro Systems to Micro Systems, The Holographic Technique (to appear).
6. Binz E., Sniatycki J. and Fischer H., The Geometry of Classical Fields, Mathematical Studies, Notas de Mathemàtica, Vol. 154, North Holland, Amsterdam 1988.
7. Folland G.B., Harmonic Analysis in Phase Space, Princeton University Press, Princeton, New Jersey 1989.
8. Greub W., Linear Algebra, Fourth Edition, Springer Verlag, New York, Berlin, Heidelberg 1975.
9. Greub W., Multilinear Algebra, Second Edition, Springer Verlag, New York, Berlin, Heidelberg 1978.
10. Greub W., Halperin S. and Vanstone R., Connections, Curvature, and Cohomology, Vol. II, Academic Press, New York and London 1973.
11. Greub W. and Petry H., Minimal Coupling and Complex Line Bundles, J. of Math. Phys., Vol. 16, No. 6 (1975).
12. Guillemin V. and Sternberg S., Symplectic Techniques in Physics, Cambridge University Press 1991.
13. Malliavin M.P. and Malliavin P., Integration on Loop Groups, I. Quasi Invariant Measures, J. of Funct. Anal., Vol. 93, 207–237 (1990).
14. Pressley A. and Segal G., Loop Groups, Oxford Science Publication, Clarendon Press, Oxford 1990.
15. Schempp W. J., Harmonic Analysis on the Heisenberg Nilpotent Lie group with Applications to Signal Theory, Pitman Research Notes in Mathematics Series, Vol. 147, Longman Scientific & Technical, London 1986.
16. Schempp W. J., Magnetic Resonance Imaging, Mathematical Foundations and Applications, Wiley-Liss, New York, Chichester, Weinheim 1998.
17. Sniatycki J., Geometric Quantization and Quantum Mechanics, Applied Math. Series, Vol. 30, Springer-Verlag, New York, Berlin, Heidelberg 1980.