Syllabus: Quantum Field Theory II

1. Path Integral Formulation of Field Theory
   1. Path Integrals in Quantum Mechanics
   2. Path Integrals in Field Theory
   3. Generating Functionals
   4. Feynman Rules for phi⁴ Theory
2. Renormalization
   1. Regularization
      1. Cutoffs
      2. Dimensional Regularization
      3. Infinities in classical and quantum theory
   2. Renormalization of QED
      1. Electron Self Energy
      2. Vacuum Polarization
      3. The Vertex Function
      4. Superficial Degree of Divergence
      5. Modified Minimal Subtraction
      6. Other subtraction schemes
   3. The Renormalization Group
      1. The running coupling in QED
      2. The running mass in QED
      3. Scale dependence and the RGE
3. Non-Abelian Symmetries
   1. Group Theory
      1. SU(2)
      2. SU(3)
      3. Tensor Methods in SU(n)
      4. Young Tableau
      5. Application: Hadrons and the Quark Model
   2. Local Symmetry and non-Abelian Gauge Theories
      1. QCD
      2. SU(2)_W
   3. Path Integral Quantization of non-Abelian Gauge theories
   4. Feynman Rules for QCD
   5. Asymtotic Freedom
   6. Confinement
4. Spontaneous Symmetry Breaking
   1. Spontaneous breaking of a continuous global symmetry: Goldstone Bosons
      1. Linear Sigma Model
      2. Non-linear Sigma Model
      3. Chiral Lagrangian for pions and Kaons
   2. Spontaneous breaking of a local symmetry: Higgs Bosons
      1. Abelian Higgs Model
      2. Non-Abelian Higgs Model
      3. Electroweak Symmetry Breaking
      4. Feynman Rules for Spontaneously Broken Gauge Theories
5. The Standard Model of Particle Physics
   1. SU(3)xSU(2)xU(1)
   2. CKM Mixing Matrix
   3. The 19 Parameters of the Standard Model
   4. Decays of the W and Z Bosons
   5. e⁺e^- → Z → f⁺f^-
   6. Higgs Decay