Syllabus
Chapter 1
- Introduction and notation
- Relativistic notation
- Classical mechanics and action principle
- Classical fields and functional differentiation
- Solutions of the Klein-Gordon and Maxwell equations
- The stat mech analogue
Chapter 2
- Symmetries and Conservation Laws
- Currents for translation, Lorentz or rotational, and internal symmetries
- Lie groups, Lie algebras and representations
- Gauge invariant actions
- Poincaré group and representations
- Spinors: Lorentz properties and actions for Weyl and Dirac spinors
- Particle states and little groups
- Solutions of the Dirac equation
Chapter 3
- Canonical quantization
- 1d lattice models and the continuum and thermodynamic limits
- Relativistic scalar quantum field theories
- Quantization of the Dirac theory (3+1)
- Propagators and causality; contour prescriptions
Chapter 4
- Functional integral quantization
- Quantum mechanics; path integral representations for correlation functions; perturbation Theory
- Vacuum to vacuum transitions and time ordering
- Scalar field theories in Lorentzian and Euclidean spacetime
- The mass gap
- Schwinger-Dyson equations
- The generating functional and perturbation theory
- Feynman rules
- The S-matrix and LSZ reduction
- Tree-level scattering in the Yukawa model
- The Spectral Representation
Chapter 5
- Gauge theory quantization
- Propagators and their gauge dependence
- Functional quantization: the Faddeev-Popov method
- Gauge fixing and ghosts
- BRST quantization
Chapter 6
- One-loop Amplitudes in QED
- Dimensional regularization and the structure of UV divergences
- Vacuum polarization
- Cutkosky rules, unitarity and the non-relativistic Coulomb potential
- Fermion self-energy; pole mass and residues
- The vertex correction; structure functions and the anomalous magnetic moment