Classical Field Theory (class notes):
The SO(3) and SU(2) symmetry groups - optional review
Interaction of fields with non-relativistic matter - optional review
The SU(3) symmetry group and quarks - optional review
Lorentz group
Klein-Gordon equation
Maxwell equations
Dirac equation
Non-Relativistic Quantum Field Theory (class notes):
Second Quantization and Many-Particle Systems.
Non-Relativistic Fermions at zero temperature: ground state, spectrum of low-lying excitations.
Propagator for the Non-Relativistic Fermi Gas. Holes, particles and the analytic properties of the propagator.
Pertubation Theory and Feynman rules (Martin & Rothen)
Applications (Martin & Rothen)
Lagrangian Formulation, Symmetries and Gauge fields
(Ryder)
Lagrangian formulation of particle mechanics
The real scalar field
Complex scalar fields and the Maxwell field
Topology and the vacuum: the Bohm-Aharanov effect Canonical Quantization and Particle Interpretation (Ryder)
The real Klein Gordon Field
The complex Klein Gordon Field
The Dirac field
The Maxwell field - radiation gauge quantization
Path Integrals and Quantum Mechanics
Perturbation theory and the S-matrix
Lagrangian Formulation, Symmetries and Gauge fields
(Ryder)
Lagrangian formulation of particle mechanics
The real scalar field
Complex scalar fields and the Maxwell field
Path integral quantization and Feynman rules (Ryder;
this material may not be covered entirely)
Generating functional for scalar fields
Functional integration
Free particle Greens function
Generating functional for interacting fields theory
Generating functional for connected diagrams
Fermions and functional methods
The S-matrix and reduction formula
Pion-nucleon scattering amplitude
Scattering cross section