03618nam 22007215 450 991025004900332120230406041554.03-319-46003-X10.1007/978-3-319-46003-1(CKB)3710000001006715(DE-He213)978-3-319-46003-1(MiAaPQ)EBC6284090(MiAaPQ)EBC5592348(Au-PeEL)EBL5592348(OCoLC)1066187714(PPN)197133126(EXLCZ)99371000000100671520161124d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierLectures on Matrix Field Theory /by Badis Ydri1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XII, 352 p. 8 illus., 6 illus. in color.)Lecture Notes in Physics,1616-6361 ;9293-319-46002-1 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.Lecture Notes in Physics,1616-6361 ;929Elementary particles (Physics)Quantum field theoryMathematical physicsComputer science—MathematicsAlgebraic geometryQuantum physicsElementary Particles, Quantum Field TheoryMathematical PhysicsMathematical Applications in Computer ScienceAlgebraic GeometryQuantum PhysicsElementary particles (Physics).Quantum field theory.Mathematical physics.Computer science—Mathematics.Algebraic geometry.Quantum physics.Elementary Particles, Quantum Field Theory.Mathematical Physics.Mathematical Applications in Computer Science.Algebraic Geometry.Quantum Physics.530.14Ydri Badisauthttp://id.loc.gov/vocabulary/relators/aut957607MiAaPQMiAaPQMiAaPQBOOK9910250049003321Lectures on Matrix Field Theory2169022UNINA