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- W4286233756 abstract "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." @default.
- W4286233756 created "2022-07-21" @default.
- W4286233756 creator A5056258195 @default.
- W4286233756 date "2022-07-16" @default.
- W4286233756 modified "2023-09-23" @default.
- W4286233756 title "Deformation Quantisation via Kontsevich Formality Theorem" @default.
- W4286233756 doi "https://doi.org/10.48550/arxiv.2207.07961" @default.
- W4286233756 hasPublicationYear "2022" @default.
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