Quantization of polysymplectic manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:145

Article

Blacker, Casey¹ 

[1] East China Normal Univ, Dept Math, 500 Dongchuan Rd, Shanghai, Peoples R China

关键词: Polysymplectic manifolds;    Geometric quantization;    Moment maps;    Dirac operators;   

DOI  :  10.1016/j.geomphys.2019.103480

来源: Elsevier

【 摘 要 】

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(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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free