Course

Spontaneous symmetry breaking and the Higgs mechanism in abelian gauge theory.

Quantum phases and correlations, the thermodynamic limit, local quantum systems, quantum Ising model.

Lightning Review of Differential Geometry: Manifolds, Tensors, Exterior & Lie Derivatives.

Particle Content of the Standard Model, Renormalizability of massive gauge theories.

Quantized Hall conductance, Landau levels for graphene

Non-abelian gauge theory: quantization and normalization

Landau levels, fractional quantum Hall effect and composite fermions, quantized Hall conductance

Quantization of ghosts

Gauge fixing and Faddeev-Popov ghosts