Syllabus
A. Introduction
1. Basic particles and forces of the Standard Model
2. Scattering experiment and the concept of cross section
3. Rutherford scattering experiment, description in classical physics, interpretation of results
4. Scattering in nonrelativistic quantum mechanics, Born approximation
5. Scattering on structured target, formfactors B. Group Theory
1. Basic concepts of group theory and their representations, reducibility and irreducibility of representations, direct sum and product of groups and their representations
2. Lie groups and algebras, generator, structure constants, commutation relations, simple and semisimple albegras, adjoint representation
3. Cartan subalgebra, transition operators, roots and weights, highest weight
4. Relation between roots and weights, composition of roots, graphical representation of weights and roots
5. Simple roots of simple Lie algebras, fundamental representations
6. Weyl symmetry of weight diagrams
7. Real and complex representations of Lie algebras C. SU(2) a SU(3) Groups
1. Construction of SU(2) multiplets by means of transition operators
2. Fundamental representation of SU(2) and reduction of its direct products
3. Isospin and its physical meaning, isospin invariance of pion-nucleon interactions
4. Gell-Mann matrices, fundamental representation of SU(3)
5. Construction of SU(3) multiplets by means of transition operators
6. Basic SU(3) multiplets
7. Reduction of direct products of SU(3) multiplets D. Nonrelativistic Constituent Quark Model
1. Experimental evidence for isospin and unitary (SU(3)) symmetry of hadrons
2. Quarks as dynamical basis of SU(3) symmetry
3. Quarks composition of basic baryon and meson multiplets
4. Quarks model with spin, SU(6) symmetric wave functions of baryons, magnetic moments of baryons, constituent quark masses
5. Heavy quarks (charm and bottom), their discovery, spectrum of observed states and its theoretical description
6. Problems of constituent quark model, quark statistics, confinement
7. Concept of quark colour, semiquantitative description of coloured forces E. Parton model
1. Basis kinematic relations for elastic and inelastic scattering of leptons on nucleons
2. Elastic scattering of electron on point-like fermion
3. Elastic scattering of electron on real proton, Rosenbluthova formula, formfactors, experimental evidence about the size of proton
4. Deep inelastic scattering of electrons on nucleons, structure functions, basic experimental facts, Bjorken scaling, Callan-Gross relation
5. Basic idea of the parton model, parton distribution functions of nucleons, spin of partons, identification of charged partons with quarks
6. Experimental information on shapes of parton distribution functions, valence distribution functions, sum rules and their interpretation, evidence for neutral partons in nucleons
7. Parton model for weak interactions, helicity and chirality, universality of distribution functions
8. Space-time description of collisions of leptons with nucleons, hadronization of partons
9. Independent fragmentation model, fragmentation functions, their shapes and symmetries
10. Parton model for electron-positron collisions, angular distribution of produced hadrons
11. Drell-Yan production of dileptons in hadron-hadron collisions F. Elements of quantum chromodynamics
1. Construction of the lagrangian in Quantum Electrodynamics, principles of global and local gauge invariance, foton propagator, gauge fixing term longitudinal photon
2. Quark colour and its mathematical description, nonabelian gauge invariance, lagrangian of Quantum Chromodynamics, basic difference from QED lagrangian
3. Feynman rules in QCD, manipulation with colour matrices
4. Elementary calculations in perturbative QCD in tree approximation, elastic scattering of quarks on quarks and quarks on gluons, comparison of cross section of basic QCD binary processes
5. Gauge invariance of QCD lagrangian and three gluon vertex
6. Mass singularities and Kinoshita-Lee-Nauenberg theorem, concept of jets
7. Basic idea of the renormalization of electric and colour charges, running coupling constants, asymptotic freedom in QCD G. QCD and parton model
1. Description of hard processes in QCD
2. Method of equivalents photons in QED, concept of splitting function
3. Parton splitting in QCD, splitting functions in the lowest order, their characteristics
4. Basic idea of the factorisation of parallel singularities, definition of dressed parton distribution functions of hadrons
5. Scaling violations and its description in QCD
6. Evolution equation for parton distribution functions of hadrons, methods of solutions, form in the momentum space
Annotation
The quark model of hadrons. The parton model and the deep inelastic scattering of leptons off nucleons.
The synthesis of mentioned models in the framework of the field theory.