Syllabus: Quantum Field Theory I

1. Lagrangian Field Theory
   1. Natural Units
   2. Covariant Notation
   3. Hamilton's Principle
   4. Euler-Lagrange Equations of Motion
   5. Example: Klein Gordon Equation
2. Relativistic Lagrangians and Relativistic Wave Equations
   1. Free Scalar Fields & The Klein Gordon Equation
   2. The Dirac Equation
   3. Electromagnetism
   4. Relativistic Wave Equations for Higher Spin States
3. Symmetries and Conservation Laws
   1. Noether's theorem
   2. Currents and Charges
   3. The Energy Momentum Tensor
   4. Internal Symmetries
   5. Group Theory
      1. SU(2)
      2. Lie Groups
      3. The Lorentz Group
      4. Representations of the Lorentz Group
      5. The Poincare Group
   6. Local (Gauge) Symmetries
      1. Electrodynamics as a Gauge Principle
4. Canonical Quantization
   1. Quantization of real scalar fields
   2. Quantization of the Dirac field
   3. Quantization of the electro-magnetic field
      1. Coulomb Gauge
      2. Covariant Gauges
5. Covariant Perturbation Theory
   1. Schrodinger, Heisenberg and Interaction pictures
   2. The time-evolution operator
   3. Wick's Theorem
   4. Feynman Propagators
6. S-Matrix elements and Physical Processes
   1. The S and T matrices
   2. Decay Rates and Cross Sections
   3. The scattering cross section
   4. Feynman rules for the S-matrix
   5. Summary of the Feynman Rules for QED
   6. Phase Space and Kinematics
7. Elementary processes of quantum electrodynamics
   1. Compton Scattering (e^- + γ → e^- + γ )
   2. Muon pair production (e⁺ + e^- → μ⁺ + μ^- )
   3. Pair annihilation (e^- + e⁺ → γ + γ)
   4. Moller scattering (e^- + e^- → e^- + e^-)
   5. Bhabha scattering (e⁺ + e^- → e⁺ + e^-)
   6. ...
8. An Effective Theory of Weak Interactions
   1. The Symmetries C,P, and T
   2. Polarized Muon Decay
   3. Violation of P, and C