Detailed Programme of the Week 10/05/2020 -- 10/09/2020:

-- Classical Fields

LECT 6 -- Monday 10/05/2020 - 2h Bonciani 12:00-14:00 (Majorana) meet.google.com/rkn-mafj-mra

Fields. Lagrangian density. Least Action Principle in the case of fields and Euler-Lagrange Equations. Symmetries and Noether's Theorem. Space-time symmetries and Internal symmetries. Continuity equation. Conserved current. Conservation of the charge.

LECT 7 -- Tuesday 10/06/2020 - 2h Bonciani    8:00-10:00 (Conversi) meet.google.com/szf-gndu-pwc

Space-Time symmetries. Invariance under Lorentz transformations. Energy-momentum Tensor. Angular momentum. Scalar fields and pure inhomogeneous Poincare' transformation, conservation of four-momentum. Proper Lorents transformation and conservation of angular momentum. Symmetries and unitary transformations. Lie groups and representations.

LECT 8 -- Wednesday 10/07/2020 - 2h Bonciani    9:00-11:00 (Conversi) meet.google.com/szf-gndu-pwc

The Lie Algebra of the group. Generators. Casimirs. Unitary representations. Example: SO(2).

LECT 9 -- Thursday 10/08/2020 - 2h Bonciani   8:00-10:00 (Majorana) meet.google.com/rkn-mafj-mra

Poincare' algebra. Finite dimensional irriducible representations of the Poincare' group. SU(2)xSU(2) and (1/2,0)+(0,1/2).

LECT 10 -- Friday 10/09/2020 - 2h Bonciani 8:00-10:00 (Conversi) meet.google.com/szf-gndu-pwc

Scalar field. Tensorial representations, vector representations and examples of the generators in this representation. SO(3,1). Rotations, SO(3) and SU(2), spinors, Pauli matrices, boosts in the 2-dimensional representation. L- and R-spinors. Parity and Dirac spinors. One-particle states. Pauli-Lubanski vector. Massive and massless particles. Helicity. Infinite dimensional representations of the Poincare' group.