Strongly Correlated Systems in Condensed Matter Physics
This MIT OpenCourseWare graduate course builds the theoretical toolkit for describing many-body quantum phenomena in condensed matter. Lectures develop the Hamiltonian second-quantized operator formalism, Green's functions, path integrals, functional integrals, and the quantum kinetic equation, then apply them to real problems in strongly correlated systems. Along the way students work through the random phase approximation, mean field theory (also called the saddle-point or semiclassical approximation), tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integrals, and the renormalization group. The course assumes a solid grounding in quantum mechanics and statistical physics and is aimed at students heading into condensed matter theory research. Materials include lecture notes and problem sets covering each technique, following the structure MIT uses in its physics graduate curriculum. As with other MIT OpenCourseWare offerings, all materials are free to access online under a Creative Commons license, with no certificate offered since this is a self-study archive of an actual MIT graduate course rather than an interactive platform course.