Non-Abelian reduction in deformation quantization
We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turn...
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| Format: | Others |
| Language: | English |
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Universität Potsdam
1997
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| Online Access: | http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25101 http://opus.kobv.de/ubp/volltexte/2008/2510/ |
| Summary: | We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant
deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved). |
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