Deformation quantization of symplectic vector fields
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910019336798208 |
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| author | Gao, Haoyuan |
| author_facet | Gao, Haoyuan |
| contents | In this paper, we study deformation quantization of symplectic vector fields à la Fedosov. We show that each symplectic vector field can be quantized to a derivation of the deformed star algebra. Moreover, we show that this quantization yields a non-abelian $2$-cocycle on the Lie algebra of symplectic vector fields with values in the deformed star algebra. Therefore, we can quantize any Lie algebra action by symplectic vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10988 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformation quantization of symplectic vector fields Gao, Haoyuan Quantum Algebra Mathematical Physics Symplectic Geometry In this paper, we study deformation quantization of symplectic vector fields à la Fedosov. We show that each symplectic vector field can be quantized to a derivation of the deformed star algebra. Moreover, we show that this quantization yields a non-abelian $2$-cocycle on the Lie algebra of symplectic vector fields with values in the deformed star algebra. Therefore, we can quantize any Lie algebra action by symplectic vector fields. |
| title | Deformation quantization of symplectic vector fields |
| topic | Quantum Algebra Mathematical Physics Symplectic Geometry |
| url | https://arxiv.org/abs/2602.10988 |