Hitchin’s connection in metaplectic quantization | Zendy

Jørgen Ellegaard Andersen | Zendy; Niels Leth Gammelgaard | Zendy; Magnus Roed Lauridsen | Zendy

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Hitchin’s connection in metaplectic quantization

Author(s) -

Jørgen Ellegaard Andersen,

Niels Leth Gammelgaard,

Magnus Roed Lauridsen

Publication year - 2012

Publication title -

quantum topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.763

H-Index - 16

eISSN - 1663-487X

pISSN - 1664-073X

DOI - 10.4171/qt/31

Subject(s) - mathematics , symplectic geometry , moduli space , connection (principal bundle) , geometric quantization , symplectic manifold , pure mathematics , differential geometry , cohomology , chern class , quantization (signal processing) , manifold (fluid mechanics) , hilbert space , algebra over a field , quantum , canonical quantization , geometry , mechanical engineering , physics , algorithm , quantum mechanics , quantum gravity , engineering

We give a differential geometric construction of a connection, which we call the Hitchin connection, in the bundle of quantum Hilbert spaces arising from metaplectically corrected geometric quantization of a prequantizable, symplectic manifold, endowed with a rigid family of Kähler structures, all of which give vanishing first Dolbeault cohomology groups. This generalizes work of both Hitchin, Scheinost and Schottenloher, and Andersen, since our construction does not need that the first Chern class is proportional to the class of the symplectic form, nor do we need compactness of the symplectic manifold in question. Furthermore, when we are in a setting similar to the moduli space, we give an explicit formula and show that this connection agrees with previous constructions. Mathematics Subject Classification (2010). 53D50, 32Q55.

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