Course

Peierl's theorem; Fermi surface; relative importance of average KE vs. average PE; density of states; Mean Field Theory.

Perturbation theory for φ4 theory, Feynman diagrams

Tight binding model; Nearly free electrons (unperterbed solution, zone folding, brief discussion of unperturbed solution).

Wick's theorem, UV and IR divergences in the free scalar propagator, Operator product expansion

Electrons in a periodic potential; Bravais lattice; Bloch's theorem; FIrst Brillouin Zone; Intro to nearly free electrons and tight binding model.

Hamiltonian in second quantization.

Functional integral quantization of free scalar field

Motivation; single-particle Schroedinger Eqn; N particles; symmetrizaion/anti-symmetrization; second quantization; Fock space.

Euclidean time, Path integral for non-relativistic particle