Springer International Publishing AG Lectures on Matrix Field Theory 1st ed. 2017

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. Autorid: Badis Ydri