Invariant Measures on Polarized Submanifolds in Group Quantization

Abstract

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.

20 pages, plain LateX

References in corpus (3)

• Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory
• Group Quantization on Configuration Space: Gauge Symmetries and Linear Fields
• Higher-Order Differential Operators on a Lie Group and Quantization

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