Bibliographic Details
| Title: |
Bargmann–Fock Sheaves on Kähler Manifolds. |
| Authors: |
Chan, Kwokwai1 (AUTHOR), Conan Leung, Naichung2 (AUTHOR), Li, Qin3 (AUTHOR) liqin@sustech.edu.cn |
| Superior Title: |
Communications in Mathematical Physics. Dec2021, Vol. 388 Issue 3, p1297-1322. 26p. |
| Subject Terms: |
*SYMPLECTIC manifolds, *GEOMETRIC quantization, *SHEAF theory, *ALGEBRA |
| Abstract: |
Fedosov used flat sections of the Weyl bundle on a symplectic manifold to construct a star product ⋆ which gives rise to a deformation quantization. By extending Fedosov's method, we give an explicit, analytic construction of a sheaf of Bargmann–Fock modules over the Weyl bundle of a Kähler manifold X equipped with a compatible Fedosov abelian connection, and show that the sheaf of flat sections forms a module sheaf over the sheaf of deformation quantization algebras defined (C X ∞ [ [ ħ ] ] , ⋆) . This sheaf can be viewed as the ħ -expansion of L ⊗ k as k → ∞ , where L is a prequantum line bundle on X and ħ = 1 / k . [ABSTRACT FROM AUTHOR] |
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| Database: |
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