Michal Praszalowicz:
Standard Model I: QCD 2021
Lectures on Tuesdays, 8:30-10:00, A-2-01
Problem classes on Wednesdays, 15:15-16:45, A-1-04
ATTENTION
Additional problem class will take place on Thursday, December 2
, at 11:30, room D-02-2
Next lecture will take place on Thursday, November 18, at 11:30, room D-02-2
On Wednesday, November 3 we will have a lecture instead of tutorials.
Next tutorials will be on November 10.
First lecture will take place on Tuesday, October 5, 2021.
A: Perturbative QCD
1. Introduction, why QCD.
2. Field theory, Feynman rules (reminder).
3. Nonabelian SU(N) field theory, free case, interaction, color factors.
4. Renormalization, example: self-energy.
5. Running coupling constant.
6. Perturbative calculation of axial anomaly.
B: Path integral formulation of QCD
1. Introduction, reminder on the Dirac notation, path integral in QM.
2. Path integral for a classical scalar field, 2-point Green function,
propagator in momentum space.
3. Fermions, functional determinants, Grassmann variables, Berezin integral.
4. Chiral transformation and its Jacobian.
5. Computing anomaly with the Fujikawa method, Atiyah-Singer theorem.
6. Theta term in QCD, topological current K_{mu}, fermion masses and theta term.
7. Quantization of the non-Abelian gauge theories: QCD vs. QED, Feynman rules, gauge fixing,
Jacobian in the path integral.
8. Faddeev-Popov ghosts, Feynman rules for ghosts, on-shell Ward identities for QCD.
9. Lattice QCD.
C: Low energy QCD
1. Effective QCD: chiral symmetry, conserved currents and charges, chiral algebra, inclusion of quark masses.
2. Chiral Ward identities, QCD spectrum and chiral symmetry, quark condensate and Goldstone bosons, PCAC.
3. Nonlinear realization of chiral symmetry and Goldstone bosons, chiral lagrangian.
4. Heavy Quark Symmetry.
Exam problems
Mail: Michal Praszalowicz