Overview
- 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
Part of the book series: Lecture Notes in Physics (LNP, volume 929)
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Table of contents (6 chapters)
Keywords
About this book
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.
Reviews
Authors and Affiliations
About the author
Research directions: Renormalization group equation and Monte Carlo method for matrix and non-commutative field theories. Emergent physics (gauge, matter, gravity, time, etc.) and emergent geometry from matrix models. Cosmological Yang-Mills models. AdS/CFT and Yang-Mills matrix models.
Other interests include stringtheory, causal dynamical triangulation, Horava-Lifshitz gravity, and supersymmetric gauge theory in four dimensions.His hobbies are reading philosophic works and history of science.
Bibliographic Information
Book Title: Lectures on Matrix Field Theory
Authors: Badis Ydri
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/978-3-319-46003-1
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2017
Softcover ISBN: 978-3-319-46002-4Published: 30 November 2016
eBook ISBN: 978-3-319-46003-1Published: 22 November 2016
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: XII, 352
Number of Illustrations: 2 b/w illustrations, 6 illustrations in colour
Topics: Quantum Field Theories, String Theory, Mathematical Physics, Math Applications in Computer Science, Algebraic Geometry, Quantum Physics