Lectures on Matrix Field Theory

Description

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. Front Matter....Pages i-xii Introductory Remarks....Pages 1-18 The Noncommutative Moyal-Weyl Spaces R θ d ....Pages 19-71 The Fuzzy Sphere....Pages 73-118 Quantum Noncommutative Phi-Four....Pages 119-206 The Multitrace Approach....Pages 207-275 Noncommutative Gauge Theory....Pages 277-313 Back Matter....Pages 315-352