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.

Badis Ydri, currently a Professor of theoretical particle physics, teaching at the Institute of Physics, Badji Mokhtar ?Annaba University, Algeria, received his PhD (2001) from Syracuse University, NY, USA, and his Habilitation (2011) from?Annaba University, Algeria. He is also a research associate at the Dublin Institute for Advanced Studies, Ireland.?His post-doctoral experience comprises a Marie Curie fellowship (2006-2008) at Humboldt University Berlin, Germany, and a Hamilton fellowship (2001-2005) at the Dublin Institute for Advanced Studies, Ireland, and a regular ICTP associate at the Abdus Salaam Center for Theoretical Physics, Trieste, Italy.
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 string theory, causal dynamical triangulation, Horava-Lifshitz gravity, and supersymmetric gauge theory in four dimensions.