Michal Praszalowicz:
Standard Model I: QCD 2025
Tutorials: Tuesday, 13:30, A-0-15
Lectures: Wednesday, 11:30, F-1-04


Wednesday's classes will be held in room B-2-01 at 11:15.
Next problem class will be in Wednesday, November 12.

Assessment

Students are required to actively participate in the problem classes.
At least three presentations of solutions to problems at the blackboard are required.

At the end of the course, a list of problems for an oral exam will be posted.
Students have to discuss two problems. Each student can propose one problem
she/he would like to discuss, and then she/he will be asked to discuss another problem
chosen by the examiner. Since problems will be rather broad, students are expected
to present structured discussion with emphasis on the line of thinking, methodology,
physical interpretetion rather than technical details.

List of topics:

A: Perturbative QCD
Introduction, why QCD.
Interactions in field theory, Feynman rules (reminder).
Nonabelian SU(N) field theory, free case, interaction, color factors.
Deep Inelastic ep scattering, Bjorken scaling.
Elastic and inelastic cross-section.
Parton model.
Renormalization, example: self-energy.
Running coupling constant.
Infrared singularities.
DGLAP evolution equations.
Perturbative calculation of axial anomaly.

B: Path integral formulation of QCD
Introduction, reminder on the Dirac notation, path integral in QM.
Path integral for a classical scalar field, 2-point Green function, propagator in momentum space.
Fermions, functional determinants, Grassmann variables, Berezin integral.
Chiral transformation and its Jacobian.
Computing anomaly with the Fujikawa method, Atiyah-Singer theorem.
Theta term in QCD, topological current K_{mu}, fermion masses and theta term.
Quantization of the non-Abelian gauge theories: QCD vs. QED, Feynman rules, gauge fixing, Jacobian in the path integral.
Faddeev-Popov ghosts, Feynman rules for ghosts, on-shell Ward identities for QCD.
Lattice QCD.

C: Low energy QCD
Effective QCD: chiral symmetry, conserved currents and charges, chiral algebra, inclusion of quark masses.
Chiral Ward identities, QCD spectrum and chiral symmetry, quark condensate and Goldstone bosons, PCAC.
Nonlinear realization of chiral symmetry and Goldstone bosons, chiral lagrangian.
Gell-Mann-Okubo mass relation, Goldberger-Treiman relation.
Heavy quarks and heavy quark spin symmetry.

Lectures

  1. 14.10.2025. Introduction, gauge symmetries, SU(N) groups, QCD lagrangian.
  2. 15.10.2025. Color factors, DIS part I.
  3. 22.10.2025. DIS part I and II, quarks and gluons as partons.
  4. 29.10.2025. Quark self energy, renormalization, running coupling constant.
    Notes on renormalization.
  5. 05.11.2025. IR singularities and evolution equations for parton densities.
  6. 19.11.2025. Axial anomaly - triangle diagrams,
    Notes on anomaly
    Path integrals in QM I.
  7. 26.11.2025. Path integrals in QM II, transition amplitudes, functional integral for a scalar field, Grassmann variables.
  8. 03.12.2025. Axial anomaly, Fujikawa method.
  9. 10.12.2025. Atiyah-Singer theorem, topology of gauge fields.


Problems

  1. 21.10.2025. Set #1.
  2. 28.10.2025. Set #2.
  3. 04.11.2025. Set #3.
  4. 12.11.2025. Set #4.
  5. 18.11.2025. Set #5.
  6. 25.11.2025. Set #6.
  7. 02.12.2025. Set #7.
    Notes on path integrals in QM
  8. 09.12.2025. Set #8.
  9. 16.12.2025. Set #9.


Mail: Michal Praszalowicz