Lectures on Matrix Field Theory [Paperback]

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries.

The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text.

Primarily written as a self-study guide for postgraduate students  with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications  these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.

Preface.-?Introductory Remarks.- The Non-Commutative Moyal-Weyl Spaces Rd.- The Fuzzy Sphere.- Quantum?Non-Commutative Phi-Four.- The Multitrace Approach.-?Non-Commutative Gauge Theory.- Appendix A - The Landau States.- Appendix B - The Traces TrtAtB and TrtAtBtCtD.- Index.The book collects almost all that has been achieved on the topic within the recent years, including all major results of many authors. As such, it is a nice reference work for graduate students and beginning researchers who want to pursue research in this area. Having all the results and different approaches collected in one place, together with the exhaustive list of references make this a valuable compendium to everyone working on noncommutative models of quantum field theory. (Andrzej Sitarz, zbMATH 1371.81013, 2017)

Badis Ydri, currently a Professor of theoretical particle physics, teaching al#S