Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T15:15:00.672Z Has data issue: false hasContentIssue false

On the quantization of quadratic momenta

Published online by Cambridge University Press:  17 February 2009

Izu Vaisman
Affiliation:
Department of Mathematics, University of Haifa, Haifa, Israel
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using geometric quantization, and accepting the quantum Hamiltonian of previous authors, we propose some candidate formulae for the quantum operator of an observable which is a quadratic form in the momenta.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Abraham, R. and Marsden, J. E., Foundations of mechanics (Benjamin-Cummings Inc., Reading, Mass., 2nd Edition, 1978).Google Scholar
[2]Cheng, K. S., “Quantization of a general dynamical system by Feynman's path integration formulation”, J. Math. Phys. 13(1972), 17231726.CrossRefGoogle Scholar
[3]de Witt, B. S., “Dynamical theory in curved spaces I”, Rev. Mod. Phys. 29(1957), 377397.CrossRefGoogle Scholar
[4]Simms, D. J. and Woodhouse, N. M. J., “Lectures on geometric quantization”, Lecture Notes in Physics 53 (Springer-Verlag, New York, 1976).Google Scholar
[5]Śniatycki, J., “Application of geometric quantization in quantum mechanics”, Lecture Notes in Mathematics 676 (Springer-Verlag, New York, 1978), 357368.Google Scholar
[6]Śniatycki, J., Geometric quantization and quantum mechanics (Springer-Verlag, Berlin, 1980).CrossRefGoogle Scholar
[7]Vaisman, I., “A coordinatewise formulation of geometric quantization”, Ann. Inst. H. Poincaré (A) 31 (1979), 524.Google Scholar
[8]Weinstein, A., “Quasi-classical mechanics on spheres”, Symp. Math. 14(1974), 2532.Google Scholar
[9]Woodhouse, N. M. J., Geometric quantization (Clarendon Press, Oxford, 1980).Google Scholar