Semi-Classical Properties of Geometric Quantization with Metaplectic Correction |
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Authors: | L Charles |
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Institution: | (1) UMR 7586 Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie-Paris 6, Paris, F-75005, France |
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Abstract: | The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of the complex structure. We show this in two ways. First, by introducing unitary identifications between the quantum spaces associated to the various complex polarizations and second, by defining an asymptotically flat connection in the bundle of quantum spaces over the space of complex structures. Furthermore Berezin-Toeplitz operators are intertwined by these identifications and have principal and subprincipal symbols defined independently of the complex structure. The relation with the Schrödinger equation and the group of prequantum bundle automorphisms is considered as well. |
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