Lectures on Matrix Field Theory

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
Cover of the book Lectures on Matrix Field Theory by Badis Ydri, Springer International Publishing
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Author: Badis Ydri ISBN: 9783319460031
Publisher: Springer International Publishing Publication: November 22, 2016
Imprint: Springer Language: English
Author: Badis Ydri
ISBN: 9783319460031
Publisher: Springer International Publishing
Publication: November 22, 2016
Imprint: Springer
Language: English

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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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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