论文标题
通过kontsevich形式定理的变形定量
Deformation Quantisation via Kontsevich Formality Theorem
论文作者
论文摘要
这项论文是肯特维奇（Kontsevich）对形式定理的证明和对泊松歧管上变形定量的分类的证明。我们从物理背景的描述开始，然后将Weyl-Moyal产品作为第一个示例。然后，我们通过差分级别的代数和$ \ mathrm {l} _ \ infty $ -Algebras来开发变形理论，这使我们能够将变形定量的分类重新化为存在$ \ mathrm {l} _ \ infty $ -quasi-isomorphism a and and a vessem lie lie lie lie Albraster的分类。接下来，我们介绍肯特维奇（Kontsevich）在$ \ mathbb {r}^d $中的形式定理的证明以及他对星星产品的构造。最后，我们简要讨论了Kontsevich Star产品在泊松歧管上的全球化。
This dissertation is an exposition of Kontsevich's proof of the formality theorem and the classification of deformation quantisation on a Poisson manifold. We begin with an account of the physical background and introduce the Weyl-Moyal product as the first example. Then we develop the deformation theory via differential graded Lie algebras and $\mathrm{L}_\infty$-algebras, which allows us to reformulate the classification of deformation quantisation as the existence of a $\mathrm{L}_\infty$-quasi-isomorphism between two differential graded Lie algebras, known as the formality theorem. Next we present Kontsevich's proof of the formality theorem in $\mathbb{R}^d$ and his construction of the star product. We conclude with a brief discussion of the globalisation of Kontsevich star product on Poisson manifolds.
