Course

Local quantum systems, quantum evolution, definition of a phase.

Orthonormal Bases, Connection, Curvature, and Cartan's Structure Equations.

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