Field Theory Methods in Condensed Matter Physics HT 2005

A: Exchange Interaction from strong Coulomb Repulsion
1. Strong Coupling expansion of the half-filled Hubbard model

B: Coherent State Path Integral for Spins

1. Single-Spin Problem
2. Berry's Phase
3. Many Spins
4. Continuum Limits

C: Quantum Ferromagnets
1. Classical Equations of Motion
2. Solution of the linearized equations

D: Quantum Antiferromagnets
1. Continuum Limit and the O(3) Nonlinear Sigma Model
2. One-Dimensional Antiferromagnets
3. Topology
4. Wilsonian RG, beta-function and anomalous dimension
5. Two-Dimensional Antiferromagnets: epsilon expansion
6. Large-N Techniques