Chapters 1,2
  • 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 3
  • Symmetries and Conservation Laws
  • Currents for translation, Lorentz or rotational, and internal symmetries
  • Lie groups, Lie algebras and representations
  • Gauge invariant actions
Chapter 4
  • PoincarĂ© group and representations
  • Spinors: Lorentz properties and actions for Weyl and Dirac spinors
  • Particle states and little groups
  • Solutions of the free Dirac equation
Chapter 5
  • 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 6
  • 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 7
  • Gauge theory quantization
  • Propagators and their gauge dependence
  • Functional quantization: the Faddeev-Popov method
  • Gauge fixing and ghosts
  • BRST quantization

Chapter 8
  • 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
Chapter 9
  • Renormalized Perturbation Theory
  • Power counting, local counterterms
  • Effective Actions
  • Background Field Methods
Chapter 10
  • Renormalized Couplings
  • The Wilson RG
  • Fixed points, RG flows, critical exponents, epsilon expansion
  • The Exact RG
  • The Beta Function in Gauge Theories
  • Chiral Anomalies
Chapter 11
  • Symmetry Breaking
  • Spontaneous Breaking of Global Symmetries, Goldstone's Theorem
  • Spontaneous Breaking of Local Symmetries, Higgs phenomena
  • Quantization and Renormalization
© 2014-23 R.G. Leigh