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Noncommutative Spacetimes

Symmetries in Noncommutative Geometry and Field Theory

  • Book
  • © 2009

Overview

Authors:
  1. Paolo Aschieri
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  2. Marija Dimitrijevic
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  3. Petr Kulish
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  4. Fedele Lizzi
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  5. Julius Wess
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Part of the book series: Lecture Notes in Physics (LNP, volume 774)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. Deformed Field Theory: Physical Aspects

    1. Front Matter

      Pages 1-1
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    2. Differential Calculus and Gauge Transformations on a Deformed Space

      • Julius Wess
      Pages 3-21

    3. Deformed Gauge Theories

      • Julius Wess
      Pages 23-37

    4. Einstein Gravity on Deformed Spaces

      • Julius Wess
      Pages 39-52

    5. Deformed Gauge Theory: Twist Versus Seiberg–Witten Approach

      • Marija Dimitrijević
      Pages 53-72

    6. Another Example of Noncommutative Spaces: κ-Deformed Space

      • Marija Dimitrijević
      Pages 73-85

  3. Noncommutative Geometries: Foundations and Applications

    1. Front Matter

      Pages 87-87
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    2. Noncommutative Spaces

      • Fedele Lizzi
      Pages 89-109

    3. Quantum Groups, Quantum Lie Algebras, and Twists

      • Paolo Aschieri
      Pages 111-132

    4. Noncommutative Symmetries and Gravity

      • Paolo Aschieri
      Pages 133-164

    5. Twist Deformations of Quantum Integrable Spin Chains

      • Petr Kulish
      Pages 167-190

    6. The Noncommutative Geometry of Julius Wess

      • Paolo Aschieri
      Pages 191-197

  4. Back Matter

    Pages 1-3
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Keywords

About this book

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 on the other handaschaptersforthepresentbook.Thesearenowharmonizedandcomplemented by a couple of contributions that have been written to provide a wider background, to widen the scope, and to underline the power of our methods.

Bibliographic Information

  • Book Title: Noncommutative Spacetimes

  • Book Subtitle: Symmetries in Noncommutative Geometry and Field Theory

  • Authors: Paolo Aschieri, Marija Dimitrijevic, Petr Kulish, Fedele Lizzi, Julius Wess

  • Series Title: Lecture Notes in Physics

  • DOI: https://doi.org/10.1007/978-3-540-89793-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2009

  • Hardcover ISBN: 978-3-540-89792-7Published: 14 July 2009

  • Softcover ISBN: 978-3-642-24249-6Published: 29 November 2011

  • eBook ISBN: 978-3-540-89793-4Published: 07 July 2009

  • Series ISSN: 0075-8450

  • Series E-ISSN: 1616-6361

  • Edition Number: 1

  • Number of Pages: XIV, 199

  • Number of Illustrations: 10 b/w illustrations

  • Topics: Mathematical Methods in Physics, Group Theory and Generalizations, Quantum Physics

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