English

A new construction of strict deformation quantization for Lagrangian fiber bundles

Symplectic Geometry 2020-03-19 v2 Mathematical Physics Differential Geometry math.MP Quantum Algebra

Abstract

We give a new construction of strict deformation quantization of symplectic manifolds equipped with a proper Lagrangian fiber bundle structure, whose representation spaces are the quantum Hilbert spaces obtained by geometric quantization. The construction can be regarded as a "lattice approximation of the correspondence between differential operators and principal symbols". We analyze the corresponding formal deformation quantization. We also investigate into relations between our construction and Berezin-Toeplitz deformation quantization.

Keywords

Cite

@article{arxiv.2003.06732,
  title  = {A new construction of strict deformation quantization for Lagrangian fiber bundles},
  author = {Mayuko Yamashita},
  journal= {arXiv preprint arXiv:2003.06732},
  year   = {2020}
}

Comments

41 pages, v2: a minor correction in the condition (U) in p.14