Invariant Measures on Polarized Submanifolds in Group Quantization

Details Invariant Measures on Polarized Submanifolds in Group Quantization Invariant Measures on Polarized Submanifolds in Group Quantization

2000-03-22

arxiv.org/abs/math-ph/0003024v1

J. Math. Phys. 41 (2000) 6747-6765

Physics

Mathematical Physics

20 pages, plain LateX

Scientific paper

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict invariance of the measures and, accordingly, the unitarity of the quantization of coadjoint orbits. As an example, the representations of $SL(2,\Real)$ are recovered.

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