Michal Praszalowicz:
Standard Model I: QCD
Lectures on Mondays, 10:00-11:45, A-1-13
Problem classes on Tuesdays, 10:15-11:45, B-2-01
From November 12 problem classes and lecture will be interchanged:
Lectures on Tuesdays, 10:15-11:45, B-2-01
Problem classes on Mondays, 10:00-11:45, A-1-13

Zagadnienia do egzaminu.

Lectures

  1. 07.10.2019. Introduction, reminder on the Dirac notation, path integral in QM.
  2. 14.10.2019. Generating functional, Euclidean amplitudes, scalar field, energy-momentum tensor for scalar field.
  3. 21.10.2019. Path integral for a classical scalar field, 2-point Green function, propagator in momentum space, functional determinants, Grassmann variables, Berezin integral.
  4. 28.10.2019. Complex Grassmann variables, naive path integral for QED, transverse and longitudinal A fields, gauge fixing and the pertinent Jacobian.
  5. 05.11.2019. Chiral transformation and its Jacobian, expressing Jacobian for an infinitensimal chiral transformation in terms of an integral, regularization by F(-D^2/M^2).
  6. 12.11.2019. Computing anomaly with the Fujikawa method, conditions for anomaly to vanish, Atiyah-Singer theorem.
  7. 19.11.2019. Theta term in QCD, topological current K_{mu}, fermion masses and theta term, link with topology, instantons in QM - intro.
  8. 26.11.2019. Instantons in QM: Eulidean path itegrals, role of the classical trajectory, quantum determinant for harmonic oscillator, dilute instanton approximation, energy splitting, zero mode of the instanton determinant.
  9. 03.12.2019. Instantons in QCD: scaling in 4 dimensions, Bogomolny bound, classical solution, quantum corrections and the role of zero modes.
  10. 10.12.2019. Quantization of the non-Abelian gauge theories: QCD vs. QED, Feynman rules, gauge fixing, Jacobian in the path integral.
  11. 17.12.2019. Faddeev-Popov ghosts, Feynman rules for ghosts, on-shell Ward identities for QCD.
  12. 07.01.2020. Effective QCD: chiral symmetry, conserved currents and charges, chiral algebra, inclusion of quark masses.
  13. 14.01.2020. Chiral Ward identities, QCD spectrum and chiral symmetry, quark condensate and Goldstone bosons, PCAC.
  14. 21.01.2020. Nonlinear realization of chiral symmetry and Goldstone bosons, chiral lagrangian.
  15. 28.01.2020. Perturbative QCD and renormalization.


Problems

  1. 15.10.2019. set#1
  2. 22.10.2019. set#2
  3. 29.10.2019. set#3
  4. 05.11.2019. set#4
  5. 18.11.2019. set#5
  6. 25.11.2019. set#6
  7. 02.12.2019. set#7
  8. 09.12.2019. set#8
  9. 16.12.2019. set#9
  10. 13.01.2020. set#10
  11. 20.01.2020. set#11
  12. 27.01.2020. Finish problems from set#11


Mail: Michal Praszalowicz