Lectures on Matrix Field Theory
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Beschreibung
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.
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.
Presents step-by-step constructions of various non-commutative and fuzzy spaces Offers an accessible explanation of various quantum properties of non-commutative scalar phi-four theory and non-commutative gauge theory Includes a detailed discussion of matrix models, multitrace, Monte Carlo and other methods used in studying fuzzy/non-commutative spaces and their matrix field theories Includes supplementary material: sn.pub/extras
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Themen in »Lectures on Matrix Field Theory«
Noncommutative field theory Noncommutative geometry Noncommutative scalar phi-four Noncommutative gauge theory Matrix models Fuzzy spaces Fuzzy physics LNP Lecture Notes in Physics Noncommutative Moyal-Weyl Spaces
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“The book collects almost all that has been achieved on the topic within the recent years, including all major results of many authors. As such, it is a nice reference work for graduate students and beginning researchers who want to pursue research in this area. Having all the results and different approaches collected in one place, together with the exhaustive list of references make this a valuable compendium to everyone working on noncommutative models of quantum field theory.” (Andrzej Sitarz, zbMATH 1371.81013, 2017)
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