•Introduction: Natural units; Elementary particles; Wave-particle duality; Conti-
nuity equation for Schr ?odinger and Klein-Gordon fields; Dirac current and antipar-
ticles
•Time-Dependent Perturbation Theory: : Decay width; Cross section; Tran-
sition amplitude: Free scalar field; Golden Rule for 2-to-2 scattering cross section;
Golden Rule for 2-body decay width
•QED: Maxwell equations; Coulomb gauge; Interaction with electromagnetic field:
Covariant derivative; Example: Coulomb scattering; Example: 2-to-2 scattering
under no external field; Vertex factors from Lagrangian; Spin-1/2; Dirac equation
and Dirac matrices; Free-particle solution to Dirac equation; Dirac equation under
external field; Charge-conjugation operator; Feynman rules for scalars and fermions;
Example: eμ → eμ and Casimir trick; Mandelstam variables; Example: e ?e → e ?e
Example: ee →ee
•Weak Interaction: Beta decay; Parity operator: τ −θ puzzle; Neutrinos; Exam-
ple: μ →e ?νe νμ and invariant integration method; Quarks and Cabibbo rotation;CP
violation and GIM mechanism; CKM matrix
•Gauge transformations: Classical fields; Lagrangian for scalars and fermions;
U(1) transformation and conserved current; Yang-Mills theory: SU(2) transforma-
tion and conserved current; Charge operator; SU(2) doublet; Charged and neutral
currents; Hypercharge and SU(2) ⊗U(1) ; Higgs field and spontaneous symmetry
breaking