Symmetry in Deformation quantization and Geometric quantization
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916439802249216 |
|---|---|
| author | Leung, Naichung Conan Li, Qin Ma, Ziming Nikolas |
| author_facet | Leung, Naichung Conan Li, Qin Ma, Ziming Nikolas |
| contents | In this paper, we explore the quantization of Kähler manifolds, focusing on the relationship between deformation quantization and geometric quantization. We provide a classification of degree 1 formal quantizable functions in the Berezin-Toeplitz deformation quantization, establishing that these formal functions are of the form $f = f_0 - \frac{\hbar}{4π}(Δf_0 + c)$ for a certain smooth (non-formal) function $f_0$. If $f_0$ is real-valued then $f_0$ corresponds to a Hamiltonian Killing vector field. In the presence of Hamiltonian $G$-symmetry, we address the compatibility between the infinitesimal symmetry for deformation quantization via quantum moment map and infinitesimal symmetry on geometric quantization acting on Hilbert spaces of holomorphic sections via Berezin-Toeplitz quantization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11311 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetry in Deformation quantization and Geometric quantization Leung, Naichung Conan Li, Qin Ma, Ziming Nikolas Differential Geometry Quantum Algebra Representation Theory In this paper, we explore the quantization of Kähler manifolds, focusing on the relationship between deformation quantization and geometric quantization. We provide a classification of degree 1 formal quantizable functions in the Berezin-Toeplitz deformation quantization, establishing that these formal functions are of the form $f = f_0 - \frac{\hbar}{4π}(Δf_0 + c)$ for a certain smooth (non-formal) function $f_0$. If $f_0$ is real-valued then $f_0$ corresponds to a Hamiltonian Killing vector field. In the presence of Hamiltonian $G$-symmetry, we address the compatibility between the infinitesimal symmetry for deformation quantization via quantum moment map and infinitesimal symmetry on geometric quantization acting on Hilbert spaces of holomorphic sections via Berezin-Toeplitz quantization. |
| title | Symmetry in Deformation quantization and Geometric quantization |
| topic | Differential Geometry Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2410.11311 |