Infinite dimensional moment map geometry and closed Fedosov’s star products
(2016) Annals of Global Analysis and Geometry — Vol. 49, n° 1, p. 1-22 (2016)
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- Abstract
- 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 (Formula presented.) of Kähler metrics in the class Θ:=[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’s 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’s star products that are closed up to order 3 in ν.
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La Fuente-Gravy, L. (2016). Infinite dimensional moment map geometry and closed Fedosov’s star products. Annals of Global Analysis and Geometry, 49(1), 1-22. https://doi.org/10.1007/s10455-015-9477-x (Original work published 2016)