Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-04T21:02:16.419Z Has data issue: false hasContentIssue false

Representations of a semi-direct product by quantization

Published online by Cambridge University Press:  24 October 2008

J. H. Rawnsley
Affiliation:
Istituto Nazionale di Fisica Nucleare (Naples Section)

Extract

1.Introduction. The purpose of this note is to apply the Kostant-Souriau quantization theory (2, 3, 4, 5, 7) to construct representations of a semi-direct product.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Arens, R.Classical Lorentz invariant particles. J. Math. Phys. 12 (1971), 24152422.CrossRefGoogle Scholar
(2)Kostant, B.Quantization and unitary representations. Lectures in Modern Analysis and Applications: III. Springer Lecture Notes 170 (1970).CrossRefGoogle Scholar
(3)Kostant, B. On certain unitary representations which arise from a quantization theory. Battelle Seattle Rencontres 1969, ed. Bargmann, V.. Springer Lecture Notes in Physics 6 (1970).Google Scholar
(4)Kostant, B. Orbits and quantization theory. Proceedings of the International Congress of Mathematicians, Nice, 1970 (Gauthier-Villars, 1971).Google Scholar
(5)Renouard, P.Variétés symplectiques et quantification. (Thèse, Orsay, 1969.)Google Scholar
(6)Simms, D. J.Lie groups and quantum mechanics. Springer Lecture Notes 52 (1968).CrossRefGoogle Scholar
(7)Souriau, J.-M.Structure des systèmes dynamiques (Dunod, 1970).Google Scholar
(8)Sternberg, S. Symplectic homogeneous spaces. Colloque Symplectique, Aix-en-Provence, 1974 (to be published by C.N.R.S.).Google Scholar