Ydri, Badis. Lectures on Matrix Field Theory [electronic resource] / / by Badis Ydri.. — 1st ed. 2017.. — XII, 352 p. 8 illus., 6 illus. in color. : online resource. — (Lecture Notes in Physics,) 929 0075-8450 ;. - Lecture Notes in Physics, 929 .
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.
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Анотація: 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.
9783319460031
10.1007/978-3-319-46003-1 doi
Quantum field theory. String theory. Mathematical physics. Computer science—Mathematics. Algebraic geometry. Quantum physics. Quantum Field Theories, String Theory. Mathematical Physics. Math Applications in Computer Science. Algebraic Geometry. Quantum Physics.