Wydział Fizyki, Astronomii i Informatyki Stosowanej

Lecture I
1. QCD as a part of the Standard Model.
2. Justification for QCD:
(a) non-abelian nature of the theory,
(b) determination of the gauge group,
(c) determination of the matter fields.
3. Abelian gauge transformations:
(a) covariant derivative,
(b) field strength tensor,
(c) Wilson line,
(d) Wilson loop.

Lecture II
1. Non-abelian gauge transformations:
(a) covariant derivative,
(b) field strength tensor,
(c) Wilson line,
(d) Wilson loop.
2. QCD Lagrangian
(a) gauge term,
(b) matter - gauge fields interaction term,
(c) mass term,
(d) CP violation term.
3. Quark masses.
4. Hierarchy of approximations for quark masses.
5. Gell-Mann - Levy approach to current conservation.
6. Global classical symmetries of the QCD Lagrangian and conserved charges
(a) U (1) baryon symmetry,
(b) U_A (1) axial symmetry,
(c) SU_V (N_f) vector symmetry,
(d) SU_A (N_f) axial vector symmetry.
7. Global symmetries of QCD at the classical and quantum level.

Lecture III - Introduction to path integrals (1)
1. Path integral formulation of quantum mechanics (QM).
2. Operator formulation of QM - time evolution operator.
3. Equivalence between operator and path integral formulation of QM.

Lecture IV - Introduction to path integrals (2)
1. Matrix elements of the time-ordered product of operators.
2. Generating functional.
3. Vacuum expectation value (VEV) of the time-ordered product of operators.
4. Generating functional for VEVs.
5. Example: harmonic oscillator and Green function.

Lecture V - Introduction to path integrals (3)
1. Path integrals in field theory.
2. Discretization of space - reduction to quantum mechanics.
3. Example: scalar field in d = 1 + 1.
4. Generating functional for Green functions.
5. Example: free scalar field in d = 3 + 1 - propagator in position and momentum space.
6. Perturbative expansion: Wick formula.
7. 1-point Green function: lowest order expansion.

Lecture VI - Introduction to path integrals (4)
1. 2- point Green function (lowest order)
2. 3 - point Green function (lowest order)
3. Feynman rules for bosonic fields with cubic and quartic interactions.
4. Generating functional for connected Green functions.
5. Truncated Green functions.
6. Self-energy.
7. Grassmann variables.

Lecture VII
1. Path integral quantization of fermions - Grassmann fields.
2. Quantization of gauge fields - gauge fixing term.
3. Faddeev - Popov determinant: ghost fields.
4. Formulation of QCD in path integral approach.

Lecture VIII
1. Feynman rules for QCD.
2. Dimensional regularization and mass scale parameter.
3. Field, mass and coupling constant renormalization in QCD.
4. Renormalization and counterterms.

Lecture IX
1. MS renormalization scheme.
2. Propagator and vertex renormalization at 1-loop level.
3. Renormalization group equations (RG) in QCD.
4. Beta function and asymptotic freedom.

Lecture X
1. QCD and dimensional transmutation.
2. Scale dependence of the quark masses.
3. Feynman rules for scattering matrix.
4. e+e¯ annihilation: lowest order.

Lecture XI
1. e+e¯  annihilation: RG improved calculation.
2. Deep Inelastic Scattering (DIS): ep → eX.
3. Factorization theorem for DIS.
4. Lowest order and parton model.

Lecture XII
1. DIS: real gluon emission.
2. Factorization scale and the leading logarithm approximation to DIS.
3. Bjorken scaling violation.
4. Factorization theorem and DGLAP equations.

Lecture XIII
1. Generators of G = SU_L(N_f) x SU_R(N_f) x U_A(1) x U(1) at the quantum level.
2. Physical states as irreducible unitary representations of G.
3. Chiral symmetry SUL(Nf) x SUR(Nf) and parity doublets.
4. Particle multiplets in experimental data (for N_f = 2).
5. Spontaneous symmetry breaking (SSB) phenomenon.
6. Wigner - Weyl and Nambu - Goldstone realization of the symmetry.
7. Goldstone theorem.
8. Chiral symmetry breaking in QCD with N_f = 2.

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