Lectures on Matrix Field Theory [electronic resource] / by Badis Ydri.
Material type: TextSeries: Lecture Notes in Physics ; 929Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Edition: 1st ed. 2017Description: XII, 352 p. 8 illus., 6 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319460031Subject(s): 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 PhysicsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 530.14 LOC classification: QC174.45-174.52Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK15664 |
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.
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.
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