Quantizable functions on Kähler manifolds and non-formal quantization

Chan，Kwokwai1; Leung，Naichung Conan2; Li，Qin3

2023-11-15

10.1016/j.aim.2023.109293

Advances in Mathematics   Impact Factor & Quartile

0001-8708

1090-2082

Applying the Fedosov connections constructed in [7], we find a (dense) subsheaf of smooth functions on a Kähler manifold X which admits a non-formal deformation quantization. When X is prequantizable and the Fedosov connection satisfies an integrality condition, we prove that this subsheaf of functions can be quantized to a sheaf of twisted differential operators (TDO), which is isomorphic to that associated to the prequantum line bundle. We also show that examples of such quantizable functions are given by images of quantum moment maps.

Deformation quantization Differential operator Geometric quantization Kähler manifold

SCI

English

Others

National Natural Science Foundation of China[12071204];Basic and Applied Basic Research Foundation of Guangdong Province[2020A1515011220];Chinese University of Hong Kong[4053400];

Mathematics

Mathematics

WOS:001078807200001

ACADEMIC PRESS INC ELSEVIER SCIENCE

MATHEMATICS

2-s2.0-85170520508

Scopus

1.Department of Mathematics,The Chinese University of Hong Kong,Shatin,Hong Kong
2.The Institute of Mathematical Sciences,Department of Mathematics,The Chinese University of Hong Kong,Shatin,Hong Kong
3.Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,China

Chan，Kwokwai,Leung，Naichung Conan,Li，Qin. Quantizable functions on Kähler manifolds and non-formal quantization[J]. Advances in Mathematics,2023,433.

Chan，Kwokwai,Leung，Naichung Conan,&Li，Qin.(2023).Quantizable functions on Kähler manifolds and non-formal quantization.Advances in Mathematics,433.

Chan，Kwokwai,et al."Quantizable functions on Kähler manifolds and non-formal quantization".Advances in Mathematics 433(2023).