PHY 7669 "Quantum Field Theory II"
Class Diary for Spring 2015


Date Notes
Wednesday 1/7 Introductions, course policies. Review of evaluation of loop integrals.
Friday 1/9 Finish review of vertex renormalization from Chapter 6.
Monday 1/12 Extra dimensions: Kaluza-Klein theories. Complex scalar field in 5 dimensions. Kaluza-Klein tower. Warped extra dimensions. Supersymmetry.
Wednesday 1/14 Section 7.1 Field Strength Renormalization. Bare parameters. Physical mass. Field-strength renormalization constant. The electron propagator: resumming the 1PI diagrams to all orders. Relation between the bare and physical parameters.
Friday 1/16 The electron self energy at one loop.
Monday 1/19 Martin Luther King Jr. Day
Wednesday 1/21 LSZ reduction formula. Relation between matrix elements and Feynman diagrams. Sec. 7.3: The optical theorem.
Friday 1/23 Unstable particles.
Monday 1/26 Sec. 7.4: The Ward-Takahashi identity - derivation.
Wednesday 1/28 Finish section 7.4: application of the Ward-Takahashi identity. Section 7.5: Renormalization of the electric charge. Tensor structure of the photon propagator. Resummation of 1PI diagrams into the photon proipagator. Begin chapter 10: Counting of UV divergences.
Friday 1/30 Superficial degree of divergence. Algebraic relations between the number of loops, vertices, electron and photon lines in a QED diagram. Formula for the superficial degree of divergence of a QED diagram in terms of the number of external photon and fermion lines. Classification of the potentially divergent diagrams in QED.
Monday 2/2 Generalization to QED in d dimensions. Renormalizable, super-reormalizable and non-renormalizable theories. Another example: phiN theory. Relation between renormalizability and the dimension of the coupling constants.
Wednesday 2/4 Renormalized perturbation theory. Bare and renormalized quantities. Counterterms. Feynman rules. One-loop structure of phi4 theory. Renormalization of the 4-point function.
Friday 2/6 Dimensional regularization (section 7.5). Renormalization of the 2-point function. Mass and wave-function renormalization.
Monday 2/9 Renormalization at higher orders.
Wednesday 2/11 The Callan-Symanzik equation. Solution to the Callan-Symanzik equation.
Friday 2/13 RGE for the scalar self-coupling in lambda phi4 theory. Solution to the RGE. Landau pole. Triviality bounds on the Higgs mass. Mass-independent renormalization schemes, minimal subtraction. Physical mass versus running mass. Alternative derivation of the RGEs.
Monday 2/16 Path integrals. Discretization.
Wednesday 2/18 Finish the proof that the path inegral amplitude satisfies the Schrodinger equation. Discussion of Homework No. 3.
Friday 2/20 Difference between Hamiltonian and Lagrangian description. Generalization to arbitrary systems. Integration over the momenta in the path integral.
Monday 2/23 No class: KM out of town (DOE panel in Washington DC)
Wednesday 2/25 No class: KM out of town (DOE panel in Washington DC)
Friday 2/27 Generating functional for the free scalar field theory. Grassmann calculus. Grassmann integrals. Functional quantization of fermions.
Monday 3/2 Spring break.
Wednesday 3/4 Spring break.
Friday 3/6 Spring break.
Monday 3/9 Discussion on final projects.
Wednesday 3/11 Non-abelian gauge theories. Covariant derivative. Transformation law of the gauge field. Field strength tensor. Transformation law of the field-strength tensor. Gauge invariant Lagrangians.
Friday 3/13 Basic facts about Lie algebras. Fndamental and adjoint representations of SU(N). Non-abelian gauge theories: application. The Standard Model. Particle representations of the SM. Gauge couplings of fermions. The beta functions of the SM. The beta functions of the MSSM.
Monday 3/16 Running of the strong coupling constant. Asymptotic freedom. Gauge coupling unification. Section 17.1. From Quarks to QCD. Section 17.2 Electron-positron annihilation into Hadrons. NLO QCD corrections.
Wednesday 3/18 Section 17.3. Deep Inelastic Scattering [individual reading]. The Parton Distribution Functions. General kinematics of pair-production.
Friday 3/20 No class: KM out of town.
Monday 3/23 No class: KM out of town.
Wednesday 3/25 Triple and quartic gauge boson couplings. W and Z boson mass spectrum. Weinberg angle.
Friday 3/27 Section 20.2. The Glashow-Weinberg-Salam Theory of Weak Interactions. Yukawa couplings in the Standard Model. W and Z branching fractions. CKM angles. Complex phases.
Monday 3/30 Yukawa sector of the SM. Higgs branching fractions. CKM angles.
Wednesday 4/1 Guest lecturer (S. Raha): Chapter 25. Dark matter.
Friday 4/3 Guest lecturer (S. Wang): Chapter 32. Passage of particles through matter.
Monday 4/6 Guest lecturer (D. Brooker): Chapter 12. CKM quark mixing matrix.
Wednesday 4/8 Guest lecturer (E. Torres): Randall Sundrum.
Friday 4/10 Guest lecturer (Y. Han): Chapter 48. Cross-section formulae for particular processes.
Monday 4/13 Guest lecturer (A. Weaver): Chapter 10. Electroweak model.
Wednesday 4/15 Guest lecturer (J. Park): Chapter 16. Grand unified theories.
Friday 4/17 Guest lecturer (S. Chakrabarty): Chapter 13. CP violation in the quark sector. Strong CP problem and axions.
Monday 4/20 Guest lecturer (P. Shyamsundar): Chapter 46. Kinematics. Transverse mass. The Cambridge MT2 variable and the Florida Smin and M2 variables.
Wednesday 4/22 Guest lecturer (S. Wilcox): Chapter 15. Quark model.