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Equivariant prequantization and admissible coadjoint orbits

Published online by Cambridge University Press:  24 October 2008

P. L. Robinson
P. L. Robinson
Affiliation:
Department of Mathematics, University of Florida, Gainesville FL32611, USA
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Extract

The orbit method has as its primary goal the construction and parametrization of the irreducible unitary representations of a (simply-connected) Lie group in terms of its coadjoint orbits. This goal was achieved with complete success for nilpotent groups by Kirillov[8] and for type I solvable groups by Auslander and Kostant[l] but is known to encounter difficulties when faced with more general groups. Geometric quantization can be viewed as an outgrowth of the orbit method aimed at providing a geometric passage from classical mechanics to quantum mechanics. Whereas the original geometric quantization scheme due to Kostant[9] and Souriau[14] enabled such a passage in a variety of situations, it too encounters difficulties in broader contexts.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 131 - 142
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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