Ydri B. Lectures on Matrix Field Theory

Springer International Publishing, 2017 — 352p. — (Lecture Notes in Physics 929) — ISBN: 978-3-319-46003-1 (eBook), 978-3-319-46002-4 (Softcover).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.Introductory Remarks
The Noncommutative Moyal-Weyl Spaces
The Fuzzy Sphere
Quantum Noncommutative Phi-Four
The Multitrace Approach
Noncommutative Gauge Theory