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