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Titlebook: Noncommutative Spacetimes; Symmetries in Noncom Paolo Aschieri,Marija Dimitrijevic,Julius Wess Book 2009 Springer-Verlag Berlin Heidelberg

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书目名称Noncommutative Spacetimes
副标题Symmetries in Noncom
编辑Paolo Aschieri,Marija Dimitrijevic,Julius Wess
视频video
概述Includes supplementary material:
丛书名称Lecture Notes in Physics
图书封面Titlebook: Noncommutative Spacetimes; Symmetries in Noncom Paolo Aschieri,Marija Dimitrijevic,Julius Wess Book 2009 Springer-Verlag Berlin Heidelberg
描述There are many approaches to noncommutative geometry and its use in physics, the ? operator algebra and C -algebra one, the deformation quantization one, the qu- tum group one, and the matrix algebra/fuzzy geometry one. This volume introduces and develops the subject by presenting in particular the ideas and methods recently pursued by Julius Wess and his group. These methods combine the deformation quantization approach based on the - tion of star product and the deformed (quantum) symmetries methods based on the theory of quantum groups. The merging of these two techniques has proven very fruitful in order to formulate ?eld theories on noncommutative spaces. The aim of the book is to give an introduction to these topics and to prepare the reader to enter the research ?eld himself/herself. This has developed from the constant interest of Prof. W. Beiglboeck, editor of LNP, in this project, and from the authors experience in conferences and schools on the subject, especially from their interaction with students and young researchers. In fact quite a few chapters in the book were written with a double purpose, on the one hand as contributions for school or conference proceedings and
出版日期Book 2009
关键词Gauge theory; Gravity; Julius Wess; deformed gauge theories; noncommuative spacetime; quantum groups
版次1
doihttps://doi.org/10.1007/978-3-540-89793-4
isbn_softcover978-3-642-24249-6
isbn_ebook978-3-540-89793-4Series ISSN 0075-8450 Series E-ISSN 1616-6361
issn_series 0075-8450
copyrightSpringer-Verlag Berlin Heidelberg 2009
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发表于 2025-3-21 22:31:51 | 显示全部楼层
Deformed Gauge Theoriesal gauge theories, but several changes are forced upon us. The Leibniz rule has to be changed such that the theory is now based on a twisted Hopf algebra. Nevertheless, this twisted symmetry structure leads to conservation laws. The symmetry has to be extended from Lie algebra valued to enveloping a
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Deformed Gauge Theory: Twist Versus Seiberg–Witten Approachormations is unchanged, but the Leibniz rule is changed (compared with gauge theories on commutative space). Consistency of the equations of motion requires enveloping algebravalued gauge fields, which leads to new degrees of freedom. In the second approach we have to go to the enveloping algebra ag
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Noncommutative Spacesefore complement the previous chapters where noncommutative spaces have been described by the commutation relations of their coordinates. The full algebraic description of ordinary (commutative) spaces requires the completion of the algebra of coordinates into a .-algebra, this encodes the Hausdorff
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Noncommutative Symmetries and Gravityacetime diffeomorphisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincaré transformations is defined and explicitly constructed. We can then define covariant derivatives (that implement the principle of general covariance on nonc
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