Noncommutative spacetimes: symmetries in noncommutative geometry and field theory

Paolo Aschieri, Marija Dimitrijevic, Petr Kulish, Fedele Lizzi, Julius Wess (auth.)3540897925, 9783540897927

There are many approaches to noncommutative geometry and to its use in physics. This volume addresses the subject by combining the deformation quantization approach, based on the notion of star-product, and the deformed quantum symmetries methods, based on the theory of quantum groups.

The aim of this work is to give an introduction to this topic and to prepare the reader to enter the research field quickly. The order of the chapters is “physics first”: the mathematics follows from the physical motivations (e.g. gauge field theories) in order to strengthen the physical intuition. The new mathematical tools, in turn, are used to explore further physical insights. A last chapter has been added to briefly trace Julius Wess’ (1934-2007) seminal work in the field.

Table of contents :
Front Matter….Pages i-xii
Front Matter….Pages 1-1
Differential Calculus and Gauge Transformations on a Deformed Space….Pages 3-21
Deformed Gauge Theories….Pages 23-37
Einstein Gravity on Deformed Spaces….Pages 39-52
Deformed Gauge Theory: Twist Versus Seiberg–Witten Approach….Pages 53-72
Another Example of Noncommutative Spaces: κ-Deformed Space….Pages 73-85
Front Matter….Pages 87-87
Noncommutative Spaces….Pages 89-109
Quantum Groups, Quantum Lie Algebras, and Twists….Pages 111-132
Noncommutative Symmetries and Gravity….Pages 133-164
Twist Deformations of Quantum Integrable Spin Chains….Pages 167-190
The Noncommutative Geometry of Julius Wess….Pages 191-197
Back Matter….Pages 1-3