書目名稱 | Quantization, Geometry and Noncommutative Structures in Mathematics and Physics | 編輯 | Alexander Cardona,Pedro‘Morales,Andrés F. Reyes Le | 視頻video | http://file.papertrans.cn/782/781030/781030.mp4 | 概述 | Inspires especially young researchers who will get a global picture and technical tools at the same time.Bridges different active areas of research in mathematics and physics.Written with a notable pe | 叢書名稱 | Mathematical Physics Studies | 圖書封面 |  | 描述 | This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics..The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics..A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt..The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andru | 出版日期 | Book 2017 | 關(guān)鍵詞 | deformation quantization; noncommutative geometry; Poisson manifold; principal fibre boundles; group act | 版次 | 1 | doi | https://doi.org/10.1007/978-3-319-65427-0 | isbn_softcover | 978-3-319-88026-6 | isbn_ebook | 978-3-319-65427-0Series ISSN 0921-3767 Series E-ISSN 2352-3905 | issn_series | 0921-3767 | copyright | Springer International Publishing AG 2017 |
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