Detailed Programme of the Week 10/07/2019 -- 10/11/2019:

-- Classical Fields

LECT 8 -- Monday 10/07/2019 - 2h Bonciani 12:00-14:00 (Majorana)

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. Representations of the Poincare' group. The Lie Algebra of the group. Generators and commutation rules.

LECT 9 -- Tuesday 10/08/2019 - 2h Bonciani 8:00-10:00 (Majorana)

Poincare' algebra. Irriducible representations of the Poincare' group. 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.

LECT 10 -- Wednesday 10/09/2019 - 2h Bonciani 10:00-12:00 (Rasetti)

One-particle states. Pauli-Lubanski vector. Massive and massless particles. 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.

Ricevimento -- Wednesday 10/09/2019 - 12:00-13:00 (uff)

LECT 11 -- Thursday 10/10/2019 - 2h Bonciani 8:00-10:00 (Majorana)

Lagrangian and Hamiltonian of the KG field. Charged scalar field and global U(1) symmetry. Charge conserved and scalar product. 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.