THEORY OF STRONG INTERACTIONS

Aim of the course is to introduce the student to the basics element of quantum-realtivistic field theory allowing them to understand the modern formulation of the fundamental interactions and in particular to strong interactions. Quantum ElectroDynamics (QED) is the abelian gauge theory that will be treated as the prototype of a fundamental interaction in quantum field theory. QuantumChromoDynamics, the theory of strong interactions is a non-abelian gauge field theory. The course has the objective to allow the student to be able to calculate explicitely the cross section for collisions between elementary particle both in QED and QCD as well lear the formalism for studying electron-proton and proton-proton collisions.

Introduction - Dimensional analysis, senergy and time scale for process under the action of the foru fundamental forces. Primer on Lorentz group. Evoltuion from relativstic quantum mechanics to quantum field theroy. Lagrangian theory for classical fields and Eulero-Lagrange equation.Hamiltonian formulation. Symmetries: internal e space-time, discrete e continous, global an local gauge. Noether Theorem. Energy-Momentum Tensor. Example for a scalr, spinorial and electromagnetic field.

Quantization of Fields - Canonical quantization for scalar, spinors and elettromagnetic fields. Spin-Statistic theorem. Interacting fields. Propagators for bosons and fermions. Pertubation theory in quantum field theory. Normal and temporal products and Wick Theorem. Definitions of S , T and M matrice and their relation to cross sections and particle decay. Feymann digramas and primer on radiative corrections. Mandelstam variables and their use for the cross section: s-channel, t-channel ed u-channel. Crossing symmetry. Link of non-relativistic Bron approximation and leading order diagram in quantum field theory.

Quantum ElecttroDynamics– QED - Gauge field, minimal coupling and QED formualtion. Feynmann rules for QED. Coulomb Scattering for elettrons e positrons and non-relativistic reduction to Rutherford cross section; Electron scattering: Moeller cross section; Scattering elettron-positron: Babbha scattering; Scattering Compton and its Ultra-relativistic limit (production of energetic photons by laser).

Quantum Chromodynamics- QCD - Introduction to Stron Interactions and QCD lagragian; some proof for quarks and their flavor and color. on abelian gauge interaction in SU(2) e extension to SU(3). Non abelian bosonic tensor. Feynmann diaggrams in QED e QCD. Asymptotic freedom and Confinement. Chiral symmetry and transition from adronic matter to a plasma of quarks and gluons. Nuclear Interaction as meson exchange and Quantum HadroDinamics (QHD). Noon-perturbative phenomena of strong interactions. Deep-inelastic collisions and form factors and parton model. Derivation of Rosenbluth formula for hadronic scatterings: electric and magnetic form factors. Bjorken scaling and parton distribution functions. QCD diagrams at leading order (qq→qq, gg→gg, qg→qg …) and cross section evaluation for elementary processes at ultra-relativistic energies. Calcualtion of hadronic spectra proton-proton, proton-nucleus e nucleus-nucleus collisions at relativistic energy.

1) F. Mandl and G. Shaw, Quantum Field Theory, Ed. Wiley- 1993

2) M. Maggiore, A Modern Introduction to Quantum Field Theory, Ed. Oxford University Press-2005

3) F.Halzen and A.D.Martin, Quarks and leptons: an introductory course in particle physics, Ed. Wiley 1984

4) M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory, Ed. Westview Press- 1995

5) J. D. Walecka, Theoretical Nuclear and Subnuclear Physics, 2nd Edition, Ed. World Scientific 2004.

6) G. Sterman et al., “Handbook of Perturbative QCD”, Review of Modern Physics 67 (1995) 158.