Quantum Field Theory in Large N Wonderland: Three Lectures

Abstract

In these lecture notes, I review how to use large N techniques to solve quantum field theories in various dimensions. In particular, the case of N-dimensional quantum mechanics, non-relativistic cold and dense neutron matter, and scalar field theory in four dimensions are covered. A recurring theme is that large N solutions are fully non-perturbative, and can be used to reliably access quantum field theory for parameter regions where weak-coupling expansions simply fail.

Comments: 54 pages, 5 figures, notes for lectures delivered at 63rd Cracow School of Theoretical Physics; v2: slightly expanded, added references; v3: typos corrected, more references