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arXiv · 1905.12961

Quantization of Polysymplectic Manifolds

Casey Blacker
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Abstract

We adapt the framework of geometric quantization to the polysymplectic setting. Considering prequantization as the extension of symmetries from an underlying polysymplectic manifold to the space of sections of a Hermitian vector bundle, a natural definition of prequantum vector bundle is obtained which incorporates in an essential way the action of the space of coefficients. We define quantization with respect to a polarization and to a spin$^\text{c}$ structure. In the presence of a complex polarization, it is shown that the polysymplectic Guillemin-Sternberg conjecture is false. We conclude with potential extensions and applications.

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Casey Blacker. 2019-07-31. Quantization of Polysymplectic Manifolds. https://doi.org/10.1016/j.geomphys.2019.103480

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