INGLESE

English

Synthetic Program:
1) Elastic scattering
2) Identity of particles
3) Relativistic Quantum Mechanics
4) Introduction to the Quantum Field Theory
5) The Klein-Gordon field
6) The Dirac field
7) Perturbation Theory
8) Feynman Diagrams
9) Quantum Electrodynamics
10) Path integrals methods

General reference books
- Quantum Mechanics (non-relativistic theory)- Authors: L. D. Landau, E. M. Lifshitz, Elsevier.
- Modern Quantum Mechanics - Authors: J. J. Sakurai, J. Napolitano, Cambridge University Press.
- An Introduction to Quantum Field Theory - Author: M. E. Peskin, D. V. Schroeder, CRC Press.

Text for recalls in Classical Electromagnetism:
- Classical Electrodynamics - Author: J. D. Jackson, John Wiley & sons, New York.

LEARNING OUTCOMES:
Students should acquire a general understanding of electrodynamics quantum mechanics and its basic principles. In particular, at the end of the course, they should be familiar with 1) the link between conserved quantities and symmetries in quantum mechanics, 2) scattering theory and 3) relativistic quantum mechanics.

KNOWLEDGE AND UNDERSTANDING:
Students will also need to understand how the covered topics come out from the basic principles of electrodynamics and quantum mechanics and the empirical data. The verification of knowledge and understanding is done written and oral tests.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Students should acquire the ability the skills to solve quantum mechanical problems related to the topics listed in the learning outcomes.

MAKING JUDGEMENTS:
It is required the ability to select the best approach to solve electrodynamics and quantum mechanical problems.

COMMUNICATION SKILLS:
It is required the ability to communicate and explain the knowledge acquired to an audience with the prerequisites of present course.

LEARNING SKILLS:
The possibility will be given to deepen some topics covered by means of textbooks and monographs and scientific articles, if required by the interest and understanding. The ability to manage existing scientific literature on the topics covered is required.

Basic knowledge of Quantum Mechanics

The course is structured in 56 hours of frontal lectures and
12 hours for classroom exercises.
It is highly recommended to attend the classes, but not compulsory, and interact with the teacher.
The course includes classes using the blackboard. Educational material will also be provided for further study after the classes

During the course the students’ assessment will be performed by a written tests that includes one or two problems about topics that have been covered during a specific segment of the course. Students will be allowed consulting one specific text during the written tests.If the outcome of these tests will not be overall satisfactory, it is mandatory to pass a written test including problems about all topics covered during the course.
Finally, students will take an oral test. The final grade will be expressed in thirtieths.

Detailed Program
1) Elastic scattering:
the scattering amplitude, Born’s formula, phase shifts and partial waves.
2) Identical particles:
the principle of indistinguishability of identical particles, exchange interaction, symmetry with respect to interchange, second quantization: Bose and Fermi statistics.
3) Relativistic Quantum Mechanics: historical introduction, Klein-Gordon and Dirac equations, quantum Lorentz transformations, symmetries of the Dirac Equation: angular momentum, parity, charge conjugation, and time reversal.
4) Introduction to Quantum Field Theory:
field theory, perspective, elements of classical field theory: lagrangian and hamiltonian field theory, Noether’s theorem.
5) The Klein-Gordon field:
Klein-Gordon field as harmonic-oscillators, causality, the Klein-Gordon propagator.
6) The Dirac field:
Lorentz invariance in wave equations, Weyl spinors, free-particle solutions of the Dirac equation, quantization of the Dirac field.
7) Perturbation Theory: perturbation expansion of correlation functions, Wick’s theorem.
8) Feynman Diagrams:
cross-section and the S-matrix, derivation of the rules, S-matrix from Feynman diagrams, Yukawa theory, the Coulomb potential.
9) Quantum Electrodynamics:
e+ e- -> mu+ mu- scattering, crossing symmetry, Compton scattering.
10) Path integrals methods: general formula of path integrals, integral formula of path integrals within lagrangian formalism.