Physics

ANGELO ESPOSITO
ANGELO ESPOSITO

GENERAL OBJECTIVES:
The goal of the course is the study of the foundations of Quantum Field Theory, starting from thee quantization of the free fields up to the introduction of the interaction of the Dirac field with the electromagnetic field (QED) and to the definition and calculation of a cross section at tree-level in perturbation theory.
The student will acquire the basic concepts of the quantization of the fields and he will be able to apply the Feynman rules for the calculation of a cross section at tree-level.
The know-how that the student acquires attending this course is indispensable for the advanced courses in Quantum Field Theory, in particular for the curriculum in Particle and Astroparticle Physics.

SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) Knowing the basis of the theory of classical and quantum fields, Lagrangian and Hamiltonian description. To be able to discuss the symmetries of a physical system and, accordingly, the conserved quantities.
OF 2) Understanding the basis of the canonical quantization and its applications to the free and interacting fields. To understand the scattering matrix.
OF 3) Knowing the definition and the basis of the calculation of a cross section.
B - Application skills
OF 5) Knowing the Feynman rules for the interaction of the Dirac and Electromagnetic fields (QED) and to be able to theoretically predict a cross section for a QED process at the tree-level in peruturbation theory.
C - Autonomy of judgment
OF 8) To be able to integrate the knowledge acquired in order to apply it in the more general context of Quantum Field Theory, renormalization and general higher-orders calculations in perturbation theory.
D - Communication skills
OF 10) Ability to discuss about the quantum theory of fields with the appropriate rigor and understanding of the approximations used

E - Ability to learn
OF 11) To be able to read independently scientific texts and articles in order to elaborate on the topics introduced in the course.

Understanding of fundamental concepts of relativistic field theory such as: Fock space and creation/annihilation operators, scattering theory and S-matrix, microcausality, basics of group theory, finite-dimensional representations of the Lorentz group, classical field theory, symmetries and conserved quantities, scalar fields, fermionic fields, massless vector fields, Quantum Electrodynamics and its non-relativistic limit.

Understanding of quantum mechanics concepts: fermions and bosons, evolution of a quantum state, spin, action of rotations on quantum states with defined spin.
Understanding of special relativity concepts: principle of relativity, Lorentz transformations, length contraction, time dilation, and some basics of Lorentz indices.
Understanding of analytical mechanics concepts: Hamiltonian and Hamilton's equations, Lagrangian and Euler-Lagrange equations.
Understanding of advanced mathematics concepts: linear algebra, distribution theory, Green's functions, and partial differential equations.

In-person blackboard lectures.

In-person.