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arXiv · 2602.10988

Deformation quantization of symplectic vector fields

Haoyuan Gao
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Abstract

In this paper, we study deformation quantization of symplectic vector fields \`a 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.

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BibTeXRIS

Haoyuan Gao. 2026-02-11. Deformation quantization of symplectic vector fields. https://arxiv.org/abs/2602.10988

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