| Date |
Notes |
| Wednesday 1/5 |
Introductions, course policies. Review of final exam.
Phi cubed in 6 dimensions.
|
| Friday 1/7 |
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.
|
| Monday 1/10 |
The electron self energy at one loop.
|
| Wednesday 1/12 |
Extra dimensions: Kaluza-Klein theories.
Complex scalar field in 5 dimensions. Kaluza-Klein tower.
|
| Friday 1/14 |
Finish review of final exam: invariant mass distributions,
bump hunting for resonances, narrow width approximation.
Angular distributions and spin. Energy dependence of the
production cross-section near threshold and spin.
|
| Monday 1/17 |
Martin Luther King Jr. Day
|
| Wednesday 1/19 |
LSZ reduction formula. Relation between matrix elements and Feynman diagrams.
Justification for the subtraction procedure for the F1 form factor.
|
| Friday 1/21 |
Sec. 7.3: The optical theorem. Unstable particles.
|
| Monday 1/24 |
Sec. 7.4: The Ward-Takahashi identity.
|
| Wednesday 1/26 |
No class: KM out of town.
|
| Friday 1/28 |
No class: KM out of town.
|
| Monday 1/31 |
Finish section 7.4: application of the Ward-Takahashi identity.
Begin 7.5: Renormalization of the electric charge.
Tensor structure of the photon propagator.
|
| Wednesday 2/2 |
Resummation of 1PI diagrams into the photon proipagator.
Begin chapter 10: Counting of UV divergences. Superficial degree of divergence.
Algebraic relations between the number of loops, vertices,
electron and photon lines in a QED diagram.
|
| Friday 2/4 |
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 2/7 |
Generalization to QED in d dimensions. Renormalizable, super-reormalizable and
non-renormalizable theories. Another example: phiN theory.
|
| Wednesday 2/9 |
Relation between renormalizability and the dimension of the coupling constants.
|
| Wednesday 2/9 |
Make-up class:
Renormalized perturbation theory. Bare and renormalized quantities.
Counterterms. Feynman rules.
|
| Friday 2/11 |
One-loop structure of phi4 theory. Renormalization of the 4-point function.
Dimensional regularization (section 7.5).
|
| Monday 2/14 |
Renormalization of the 2-point function. Mass and wave-function renormalization.
|
| Wednesday 2/16 |
No class: KM out of town.
|
| Friday 2/18 |
Renormalization at higher orders.
|
| Monday 2/21 |
Dark matter. Boltzmann equation.
|
| Wednesday 2/23 |
Continue with the solution to the Boltzmann equation.
|
| Friday 2/25 |
Finish the derivation of the DM relic density.
|
| Monday 2/28 |
Spring break.
|
| Wednesday 3/2 |
Spring break.
|
| Friday 3/4 |
Spring break.
|
| Monday 3/7 |
The Callan-Symanzik equation.
|
| Wednesday 3/9 |
Solution to the Callan-Symanzik equation.
|
| Friday 3/11 |
RGE for the scalar self-coupling in lambda phi4 theory.
Solution to the RGE. Landau pole.
Triviality bounds on the Higgs mass.
|
| Monday 3/14 |
Mass-independent renormalization schemes, minimal subtraction.
Physical mass versus running mass. Alternative derivation of the RGEs.
|
| Wednesday 3/16 |
Discussion on final projects.
|
| Friday 3/18 |
Path integrals. Discretization.
|
| Monday 3/21 |
Finish the proof that the path inegral amplitude satisfies
the Schrodinger equation. Discussion of Homework No. 3.
|
| Wednesday 3/23 |
Difference between Hamiltonian and Lagrangian
description. Generalization to arbitrary systems.
Integration over the momenta in the path integral.
|
| Friday 3/25 |
Generating functional for the free scalar field theory.
|
| Monday 3/28 |
Grassmann calculus. Grassmann integrals.
Functional quantization of fermions.
|
| Wednesday 3/30 |
Non-abelian gauge theories. Covariant derivative.
Transformation law of the gauge field. Field strength tensor.
|
| Friday 4/1 |
Transformation law of the field-strength tensor.
Gauge invariant Lagrangians.
|
| Monday 4/3 |
Basic facts about Lie algebras. Fndamental and adjoint representations of SU(N).
|
| Wednesday 4/6 |
Non-abelian gauge theories: application. The Standard Model.
Particle representations of the SM. Gauge couplings of fermions.
|
| Friday 4/8 |
Triple and quartic gauge boson couplings. The beta functions of the SM.
Running of the strong coupling constant. Asymptotic freedom. Gauge coupling
unification. Yukawa couplings in the Standard Model.
|
| Monday 4/11 |
The Effective Potential (G. Boyd).
Section 11.3. The Effective Action.
Section 11.4. Computation of the Effective Action.
|
| Monday 4/11 |
Make-up class (16:00):
QCD-I (D. Kar).
Section 17.1. From Quarks to QCD.
Section 17.2. Electron-positron annihilation into Hadrons.
(Avoid references to results from Final Project of Part I.)
Section 17.3. Deep Inelastic Scattering. The Parton Distribution Functions.
|
| Wednesday 4/13 |
QCD-II (Y. Oksuzian).
Section 17.4. Hard Scattering Processes in Hadron Collisions.
|
| Friday 4/15 |
Make-up class (14:00):
The Higgs Mechanism (S. Deb).
Section 11.1. Spontaneous Symmetry Breaking. Goldstone's theorem.
Section 20.1. The Higgs mechanism. (Skip the SU(3) example in
the "Non-Abelian Examples" subsection, as well as the
"Formal Description of the Higgs Mechanism" subsection.)
|
| Monday 4/18 |
No class: APS meeting in Tampa.
|
| Wednesday 4/20 |
Special time (13:00):
Electroweak Theory (K. Kotov).
Section 20.2. The Glashow-Weinberg-Salam Theory of Weak Interactions.
(Skip "Anomaly Cancellation" and "A Higgs Sector?".)
|
| Wednesday 4/20 |
Beyond the Standard Model (Y. Pakhotin).
Section 22.2. Grand Unification and its Paradoxes.
Section 22.4. Supersymmetry. MSSM. Superpartners.
Fermionic superpartner spectrum: higgsinos and gauginos
versus neutralinos and charginos.
Interactions of the superpartners.
Section 22.5. Toward the Ultimate Theory of Nature.
|