
Course unit
THEORETICAL PHYSICS
SCP7081638, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/02 
Theoretical Physics, Mathematical Models and Methods 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Prerequisites:

Classical Mechanics. Quantum Mechanics. 
Target skills and knowledge:

The course offers a first introduction to the quantization of field theories, explaining the basic tools and formalism of quantum field theories and giving some physical applications to elementary scattering processes. 
Examination methods:

Written. Solution of one or more problems. 
Assessment criteria:

Knowledge and understanding of the course topics. Ability of solving elementary problems related to the course topics. 
Course unit contents:

1. Classical and quantum mechanics of particles.
Lagrangian, action, principle of least action, Hamiltonian, Poisson brackets, Quantization, Symmetries in Quantum Mechanics, Schroedinger, Heisenberg and interaction picture.
2. Classical field theory.
Functional derivative. Principle of least action for fields, Hamiltonian, Hamilton equations.
3. Symmetries and conservation laws.
Noether's theorem, Spacetime symmetries and conserved quantities, internal symmetries and conserved charges.
4. Scalar field.
Classical real scalar field. KleinGordon equation and solution. Canonical quantization. Normal ordering. Fock space. Microcausality.
Classical and quantum complex scalar field. Internal symmetry and conserved charge. The scalar propagator.
5. Spinors.
Lorentz group and its representations. Spinor fields. Lagrangian for a Dirac spinor field. General solution of the Dirac equation. Energy and helicity projectors. Canonical quantization for the Dirac field (and anticommutators). Fermion propagator. Minimal coupling and covariant derivative. Nonrelativistic limit, gyromagnetic factor.
6. Vector fields.
Classical vector field. Proca equation. Classical electromagnetic field theory. Gauge invariance. Lorentz gauge. Gauge fixing. Lagrangian and Hamiltonian densities in the Feynman gauge. General solution. Covariant quantization. Fock space and indefinite metric. Unphysical polarizations. GuptaBleuler condition. Propagator.
7. Interactions.
Interactions in a classical field theory. The Smatrix expansion and transition probability. Tproducts.
8. QED.
Smatrix expansion in QED. Feynman diagrams in coordinate space and in momentum space. 2>2 scattering processes. Photon and electron selfenergies. The Compton scattering. QED Feynman rules. The crosssection. 
Planned learning activities and teaching methods:

Blackboard lectures. 
Textbooks (and optional supplementary readings) 

Mandl, Franz; Shaw, Graham, Quantum field theoryFranz Mandl, Graham Shaw. Hoboken: John Wiley, 2010.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Problem solving

