dorsal/arxiv
View SchemaFedosov *-products and quantum momentum maps
| Authors | Ping Xu |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9608006 |
| URL | https://arxiv.org/abs/q-alg/9608006 |
Abstract
We study various aspects of Fedosov star-products on symplectic manifolds. By introducing the notion of "quantum exponential maps", we give a criterion characterizing Fedosov connections. As a consequence, a geometric realization is obtained for the equivalence between an arbitrary *-product and a Fedosov one. Every Fedosov *-product is shown to be a Vey *-product. Consequently, one obtains that every *-product is equivalent to a Vey * -product, a classical result of Lichnerowicz. Quantization of a hamiltonian G-space, and in particular, quantum momentum maps are studied. Lagrangian submanifolds are also studied under a deformation quantization.
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"abstract": "We study various aspects of Fedosov star-products on symplectic manifolds. By\nintroducing the notion of \"quantum exponential maps\", we give a criterion\ncharacterizing Fedosov connections. As a consequence, a geometric realization\nis obtained for the equivalence between an arbitrary *-product and a Fedosov\none. Every Fedosov *-product is shown to be a Vey *-product. Consequently, one\nobtains that every *-product is equivalent to a Vey * -product, a classical\nresult of Lichnerowicz. Quantization of a hamiltonian G-space, and in\nparticular, quantum momentum maps are studied. Lagrangian submanifolds are also\nstudied under a deformation quantization.",
"arxiv_id": "q-alg/9608006",
"authors": [
"Ping Xu"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Fedosov *-products and quantum momentum maps",
"url": "https://arxiv.org/abs/q-alg/9608006"
},
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