Reference : Infinite dimensional moment map geometry and closed Fedosov star products |
Scientific journals : Article | |||
Physical, chemical, mathematical & earth Sciences : Mathematics | |||
http://hdl.handle.net/10993/37311 | |||
Infinite dimensional moment map geometry and closed Fedosov star products | |
English | |
La Fuente-Gravy, Laurent ![]() | |
2016 | |
Annals of Global Analysis and Geometry | |
Kluwer Academic Publishers | |
49 | |
1 | |
1-22 | |
Yes (verified by ORBilu) | |
International | |
0232-704X | |
1572-9060 | |
Netherlands | |
[en] symplectic connections ; closed star product ; moment map ; deformation quantization ; Kähler manifolds | |
[en] We study the Cahen–-Gutt moment map on the space of symplectic connections of a
symplectic manifold. Given a Kähler manifold (M, ω, J ), we define a Calabi-type functional F on the space M of Kähler metrics in the class [ω]. We study the space of zeroes of F. When (M, ω, J ) has non-negative Ricci tensor and ω is a zero of F, we show the space of zeroes of F near ω has the structure of a smooth finite dimensional submanifold. We give a new motivation, coming from deformation quantization, for the study of moment maps on infinite dimensional spaces. More precisely, we establish a strong link between trace densities for star products (obtained from Fedosov-type methods) and moment map geometry on infinite dimensional spaces. As a byproduct, we provide, on certain Kähler manifolds, a geometric characterization of a space of Fedosov star products that are closed up to order 3. | |
Researchers | |
http://hdl.handle.net/10993/37311 | |
10.1007/s10455-015-9477-x |
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