Detailed Programme of the Week 10/26/2020 -- 10/30/2020:

-- Canonical Quantization

LECT 21 -- Monday 10/26/2020 - 2h Bonciani 12:00-14:00 (Majorana) meet.google.com/rkn-mafj-mra

Anti-commutation relations and positive definite energy density. Fock space, antisymmetric two-particle state and Fermi statistics. Locality and Causality. Massless fermions (Dirac neutrinos).

LECT 22 -- Tuesday 10/27/2020 - 2h Bonciani 8:00-10:00 (Conversi) meet.google.com/szf-gndu-pwc

Electromagnetic field. Maxwell's equations. Scalar and vector potentials. Gauge invariance. Covariant form of Maxwell's equations. Lorents gauge. Electromagnetic tensor and Electric-Magnetic fields equations in covariant form. Larangian density. Counting of the actual degrees of freedom in covariant form (and Coulomb gauge).

LECT 23 -- Wednesday 10/28/2020 - 2h Bonciani 9:00-11:00 (Conversi) meet.google.com/szf-gndu-pwc

Canonical Quantization of the field A^mu. Problems arising from the vanishing of the momentum conjugated to A^0. Gauge fixing. Gupta-Bleuler quantization. Plane wave solutions. Physical states. Temporal, longitudinal and transverse modes. Conditions fulfilled by the physical states. Energy and momentum densities and contribution of the physical states. The Photon.

LECT 24 -- Thursday 10/29/2020 - 2h Bonciani 8:00-10:00 (Majorana) meet.google.com/rkn-mafj-mra

Non-homogeneous differential equations and Green's function. The case of the scalar field. Fourier transform and integration in C. Closed paths. Open paths. Retarded and Advanced Green's functions. The Feynman propagator for the scalar field.

LECT 25 -- Friday 10/30/2020 - 2h Bonciani 8:00-10:00 (Conversi) meet.google.com/szf-gndu-pwc

Covariant form. Propagator as the vacuum expectation value of T-ordered product of two fields. Feynman's propagator for the spinor field and for the electromagnetic field.