Lectures on fuzzy and fuzzy SUSY physics. (English) Zbl 1132.81001
Hackensack, NJ: World Scientific (ISBN 978-981-270-466-5/hbk). xiii, 181 p. (2007).
This is a excellent book. Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes provide a comprehensive introduction to the field. In the book, starting with the construction of fuzzy spaces, using the concrete examples of the fuzzy sphere and fuzzy complex projective spaces, the authors move on to discuss the technology of star products on noncommutative R2d and on the fuzzy sphere. The authors also treat scalar, spinor and gauge field theories as well as extended objects such as monopoles and nonlinear sigma modes in considerable detail. A detailed treatment of the regularization of supersymmetry is given using the techniques of fuzzy physics.
Reviewer: Yong-Qing Chen (Shenzhen)
MSC:
81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |
81T60 | Supersymmetric field theories in quantum mechanics |
81T99 | Quantum field theory; related classical field theories |
81R60 | Noncommutative geometry in quantum theory |
54A10 | Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) |
46S40 | Fuzzy functional analysis |
47S40 | Fuzzy operator theory |