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 $\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.