Week 1: Least action principle, Noether
theorem, classical field theory, and stress-energy tensor
Week 2: Quantum mechanics and path
integrals, relationship between quantum mechanics and statistical mechanics,
1D Ising model, and transfer matrix formalism
Week 3-4: 2D Ising model, Peierls
criterion, transfer matrix formalism and Jordan-Wigner fermions, exact solution
Week 5: 2D Dirac equation, Dirac
and Majorana fermions, gauge symmetry, gauge and axial currents
Week 6: Free 1D electron gas, axial
anomaly, and bosonization
Week 7: Interacting 1D electron gas,
Tomonaga-Luttinger model