The course features the application of modern field theory methods and
especially Feynman diagrams to fermion and boson system and critical
phenomena. The initial text will be Quantum field theory and statistical
physic by Abrikosov, Gorkov and Dzyalizhinski. Also discussed will be an
introduction to scaling and the renormalization group (Wilson papers, texts of Pfeuty and Toulose, Ma and Reichl). Other topics will
include broken symmetry non-phonon mechanisms in fermion superconductivity, field theory generalizations of the independent particle or Hartree-Fock model for non-homogeneous Fermion systems, Feynman path integrals and Wiener measure in statistical physics, exact properties of the Ising model,Feynman path integrals and Wiener measure in statistical physics, onset of ferromagnetism and spin-fluctuations.