Lectures on Matrix Field Theory

  • Badis Ydri

Part of the Lecture Notes in Physics book series (LNP, volume 929)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Badis Ydri
    Pages 1-18
  3. Badis Ydri
    Pages 73-118
  4. Badis Ydri
    Pages 119-206
  5. Badis Ydri
    Pages 207-275
  6. Badis Ydri
    Pages 277-313
  7. Back Matter
    Pages 315-352

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.


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

Authors and affiliations

  • Badis Ydri
    • 1
  1. 1.Institute of PhysicsBM Annaba UniversityAnnabaAlgeria

Bibliographic information