Lectures on Matrix Field Theory I

Abstract

The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative ${\varphi }^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.

Comments: 293 pages, 10 figures. Several small parts of these lectures have already appeared in various preprints found on the arXiv. I have felt no need to reword my own expressions if I thought they conveyed the physics properly