Detailed Programme of the Week 10/12/2020 -- 10/16/2020:

-- Classical Fields

LECT 11 -- Monday 10/12/2020 - 2h Bonciani 12:00-14:00 (Majorana) meet.google.com/rkn-mafj-mra

Natural Units. Klein-Gordon (KG) Equation. Motivations. Recapitulation of Schroedinger's Equation and non relativistic QM point of view. The scalar product in L2 and its time independence. Covariance of the KG equation. Scalar product for the KG field and probability density not positive definite. Lagrangian and Hamiltonian of the KG field. Charged scalar field and global U(1) symmetry. Charge conserved and scalar product.

LECT 12 -- Tuesday 10/13/2020 - 2h Bonciani 8:00-10:00 (Conversi) meet.google.com/szf-gndu-pwc

Potential in the Lagrangian and mass term. Plane wave solutions of the KG equation. Positive and negative energy solutions. Normalization of the solutions and ortonormal basis. General solution as superposition of positive and negative energy solutions. Canonical Quantization. Conjugated momenta, Hamiltonian density, probability density. Change of perspective and quantization. Field in terms of creation and annihilation operators. Heisemberg picture, time-dependent operators, time-independent states. Hamiltonian density in normal modes.

LECT 13 -- Wednesday 10/14/2020 - 2h Bonciani 9:00-11:00 (Conversi) meet.google.com/szf-gndu-pwc

Harmonic oscillator: a recap. Creation and annihilation operators. Canonical quatization and commutation relations on the fields. Commutation relations for the creation and annihilation operators. Normal ordering. Noether's theorem and conserved quantities. Momentum in terms of creation and annihilation operators. Fock space. One-particle state. Two-particle state and Bose symmetry.

LECT 14 -- Thursday 10/15/2019 - 2h Bonciani 8:00-10:00 (Majorana) meet.google.com/rkn-mafj-mra

Charged scalar field. Energy, momentum and charge. Fock space. Particles and anti-particles.

LECT 15 -- Friday 10/16/2020 - 2h Bonciani 8:00-10:00 (Conversi) meet.google.com/szf-gndu-pwc

Locality and causality in Quantum Field Theory. Dirac equation. Properties of alpha and beta matrices. Covariance of Dirac's equation.