高阶Koszul括号的量子锚
A quantum anchor for higher Koszul brackets
AI总结：
本文针对$P_\infty$-结构，将高阶Koszul括号到Schouten括号的$L_\infty$-态射量子化为单一的形式傅里叶积分算子，并采用厚态射技术与量子Mackenzie-Xu变换。
摘要：
众所周知，在泊松流形上，de Rham复形与Poisson复形之间的链映射也将微分形式的Koszul括号映射为多向量场的Schouten括号。在$P_\infty$-结构的广义情形下，其中泊松双向量$P$被满足$[[P,P]]=0$的任意偶多向量所取代，链映射的类似物以及从高阶Koszul括号到Schouten括号的$L_\infty$-态射也是已知的；然而，它们在本质上存在显著差异。在本文中，我们解决了对这一图景进行量子化的问题。特别地，我们证明了$L_\infty$-态射被量子化为一个单一的线性算子，该算子是一个形式傅里叶积分算子。本文采用了Voronov的厚态射技术以及$L_\infty$-代数胚框架下的量子Mackenzie-Xu变换。
英文摘要：
It is well known that the chain map between the de Rham and Poisson complexes on a Poisson manifold also maps the Koszul bracket of differential forms into the Schouten bracket of multivector fields. In the generalized case of a $P_\infty$-structure, where a Poisson bivector $P$ is replaced by an arbitrary even multivector obeying $[[P,P]]=0$, an analog of the chain map and an $L_\infty$-morphism from the higher Koszul brackets into the Schouten bracket are also known; however, they differ significantly in nature. In the present paper, we address the problem of quantizing this picture. In particular, we show that the $L_\infty$-morphism is quantized into a single linear operator, which is a formal Fourier integral operator. This paper employs Voronov's thick morphism technique and quantum Mackenzie-Xu transformations in the framework of $L_\infty$-algebroids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
