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Lectures on Matrix Field Theory
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.
Philosophy and the Interpretation of Quantum Physics
Quantum mechanics is perhaps the greatest scientific breakthrough ever achieved. It brought with it a seismic paradigm shift in our way of thinking about nature, and at the same time, it underpins most of the dramatic technological innovations of the modern era, as well as providing a profound lasting impact on our metaphysical conception of reality. This book provides oversight of many views on the interpretation of quantum physics and the wide philosophical debate that still embroils this subject.
Modern Course in Quantum Field Theory
A Modern Course in Quantum Field Theory provides a self-contained pedagogical and constructive presentation of quantum field theory. Written for advanced students, the work provides complete material for a two or three semester course and includes numerous problem exercises, some with detailed solutions.
Lectures on General Relativity, Cosmology and Quantum Black Holes
"This book is a rigorous text for students in physics and mathematics requiring an introduction to the implications and interpretation of general relativity in areas of cosmology. Readers of this text will be well prepared to follow the theoretical developments in the field and undertake research projects as part of an MSc or PhD programme. This ebook contains interactive Q & A technology, allowing the reader to interact with the text and reveal answers to selected exercises posed by the author within the book. This feature may not function in all formats and on reading devices."--Prové de l'editor.
Computational Physics: An Introduction To Monte Carlo Simulations Of Matrix Field Theory
This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since 2010 to physics students at Annaba University. The second part is much more advanced and deals with the problem of how to set up working Monte Carlo simulations of matrix field theories which involve finite dimensional matrix regularizations of noncommutative and fuzzy field theories, fuzzy spaces and matrix geometry. The study of matrix field theory in its own right has also become very important to the proper understanding of all noncommutative, fuzzy and matrix phenomena. The second part, which consists of 9 simulations, was delivered informally to doctoral students who were working on various problems in matrix field theory. Sample codes as well as sample key solutions are also provided for convenience and completeness.
Matrix Models of String Theory
Written for postgraduate students as a pedagogical introduction to string theory. Extending beyond an introductory review of the subject, it encompasses key analytical and numerical tools, as well as useful physical models in applications. The book is augmented with numerous codes in addition to problems and exercises.
Particles, Fields And Topology: Celebrating A. P. Balachandran
A P Balachandran has a long and impressive record of research in particle physics and quantum field theory, bringing concepts of geometry, topology and operator algebras to the analysis of physical problems, particularly in particle physics and condensed matter physics. He has also had an influential role within the physics community, not only in terms of a large number of students, research associates and collaborators, but also serving on the editorial boards of important publications, including the International Journal of Modern Physics A.This book consists of articles by students and associates of Balachandran. Most of the articles are scientific in nature, with topics ranging from noncommutative geometry, particle physics phenomenology, to condensed matter physics. Various chapters focus on new perspectives and directions resulting from Balachandran's contributions to physics, as well as some reminiscences of collaborating and working with Balachandran.
A Modern Course in Quantum Field Theory
"A Modern Course in Quantum Field Theory provides a self-contained pedagogical and constructive presentation of quantum field theory. Here, constructive is not meant in the sense of axiomatic field theory, but it is merely used in the sense that all results must be obtained by an explicit set of calculations from accepted premises by those who start to learn this subject. Written for advanced students the work provides complete material for a two or three semester course, and includes numerous problem exercises, some with detailed solutions." -- Prové de l'editor.
An Introduction to Noncommutative Differential Geometry and Its Physical Applications
A thoroughly revised introduction to non-commutative geometry.
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
