Theory of fundamental interactions 1

A.Y. 2020/2021
Overall hours
Learning objectives
The course aims at providing an understanding of the basics of quantum field theory, and of the techniques applied for the calculation of physical processes at high energies.
Expected learning outcomes
At the end of the course will be able to
1. describe the kinematics of a physical process of interaction between particles (phase space, reference system, Mandelstam invariants)
2. calculate at tree level the cross section and the decay rate starting from the Feynman rules of the theory
3. set up a calculation to one or more loops and to understand the meaning of the renormalization procedure
4. determine the behavior of the coupling constants given the beta function of a theory, in particular in the case of QCD
5. consider the effect of radiative QCD corrections on simple physical processes
6. derive the Fermi theory of weak decays from the Weinberg-Salam theory and to relate the predictions in the respective theories
7. express the electromagnetic and weak coupling constants in terms of the Weinberg angle
Course syllabus and organization

Single session

Lesson period
Second semester
If it is not possible to deliver the lectures in presence, they will be delivered telematically via the Zoom platform according to the same scheduled times. The lessons will be recorded and will remain available to students.

The written and oral examination will be performed telematically.
Course syllabus
- Classical fields
- Classical electromagnetic field
- Quantization of the elctromagnetic field
- Quantization of the scalar field
- The scalar propagator
- Symmetries and conservation laws
- Dirac equation
- Lorentz covariance and solutions of Dirac equation
- Quantization of the Dirac filed
- The fermionic propagator
- Covariant theory of the photons and photon propagator
- Interactions and perturbation theory
- The scattering matrix expansion and the Wick theorem
- Feynman diagrams and rules for QED
- Scattering cross section and decay rate
- Gamma matrix algebra and polarizations sum
- Lepton pair production in electron-positron annihilation
- Bhabha and Compton scattering
- Scattering in external field, bremsstrhalung einfrared divergences
- Radiative corrections, divergent loop diagrams
- Regularization and renormalization, the Ward identity
- The anomalous magnetic moment

The Lagrangian of electrodynamics
- Feynman rules for quantum electrodynamics
- Calculation of the process of muon pair creation in electron-positron annihilation (e + e- -> mu + mu-) at the leading perturbative order: from Feynman diagrams to amplitudes
- Calculation of cross sections and decay widths: flux factor and phase space
- The Compton scattering: calculation at the leading perturbative order
- The "g-2" of the electron: finite one-loop corrections
- Ultraviolet divergences and renormalization
- Beta function and asymptotic freedom
- Introduction of the "color" and QCD
- QCD corrections to electromagnetic processes: hadron production in electron-positron annihilations (e + e- -> hadrons)
- Fermi's theory of beta decays and introduction to electroweak unification
Prerequisites for admission
1. Quantum Mechanics (non relativisitica theory)
2. Classical electrodynamics (including Special Relativity)
3. Foundations of Nuclear and Subnuclear Physics
Teaching methods
The teaching method consists of theory lessons on the blackboard and in the solution of exercises on the topics covered.

Written and oral exam.
Teaching Resources
-F. Mandl, G. Shaw, Quantum Field theory, Wiley.
-M. Peskin, D. Schroeder, An introduction to quantum field theory, CRC Press.
-J.J. Sakurai, Advanced Quantum Mechanics, Addison Wesley
Assessment methods and Criteria
Written homework problems with oral discussion of the solutions and of the topics covered in class.
Lessons: 42 hours
Professor: Ferrera Giancarlo