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Lectures on matrix field theory / Badis Ydri.

By: Material type: TextTextSeries: Lecture notes in physics ; v 929.Publication details: Cham : Springer, 2017.Description: xii, 352 pages : illustrations ; 23 cmISBN:
  • 9783319460024 (alk. paper)
Subject(s): DDC classification:
  • 530.14 23 Y36
Contents:
1. Introductory Remarks.- 2. The Non-Commutative Moyal-Weyl Spaces Rd.- 3. The Fuzzy Sphere.- 4. Quantum Non-Commutative Phi-Four.- 5. The Multitrace Approach.- 6. Non-Commutative Gauge Theory.
Summary: 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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Includes bibliographical references and index.

1. Introductory Remarks.-
2. The Non-Commutative Moyal-Weyl Spaces Rd.-
3. The Fuzzy Sphere.-
4. Quantum Non-Commutative Phi-Four.-
5. The Multitrace Approach.-
6. Non-Commutative Gauge 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.

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