Detailed Programme of the Week 09/23/2019 -- 09/27/2019:

-- Introduction and Special Relativity

LECT 1 -- Monday 09/23/2019 - 2h Bonciani 12:00-14:00 (Careri)

Info about the course and the exam. General introduction. Non relativistic Quantum Mechanics and Schoedinger's equation. Wave function and probability density. Description of a single particle state at low energies. The need to include Special Relativity. The Klein-Gordon equation as a relativistic wave equation. Probability density. Negative energy solutions. Attempts to get a correct relativistic wave equation. Dirac's equation. Probability density. Negative energy solutions. Hole theory and the positron. Multi particle formalism. Energy and mass. Classical Electrodynamics. Wave equations as the correct classical field equations. Second quantization.
Galilean relativity and composition of velocities in Newtonian mechanics. Maxwell's equations and Lorentz transformations. Constance of the speed of light. Attempts to reformulate a relativistically covariant version of Mechanics.

LECT 2 -- Tuesday 09/24/2019 - 2h Bonciani 8:00-10:00 (Conversi)

Einstein's postulates of relativity. Criticism of the "absolute time". Simultaneous events. Light front propagation. Invariant interval. Time-like, light-like and space-like intervals and the causality structure of Space-Time. Light cone. Lorentz transformations (derivation using homogeneity and isotropy of the Space-Time and the invariance of $ds^2$ . Boost in the x direction. General case. Limit of small velocity and the recovery of Galilean transformations.

LECT 3 -- Wednesday 09/25/2019 - 2h Bonciani 10:00-12:00 (Rasetti)

Contraction of lengths. Dilatation of time. Bruno Rossi Experiment. Transformation of the 3-velocity under Lorentz transformations and the relativistic composition of velocities. Vectors. Contravariant and covariant components.

LECT 4 -- Thursday 09/26/2019 - 2h Bonciani 8:00-10:00 (Conversi)

Transformation of contravariant and covariant components of a vector under a basis change. Scalar product. Metric tensor and its transformation under a basis change. Tensors and properties. Necessity to express Physics in terms of tensorial relations. Minkowski space $M^4$ . $\eta_{\mu \nu}$ metric tensor. Contravariant and covariant vectors in $M^4$ . Boosts and the tensorial relation that defines a boost. Dynamics of a classical free particle and covariant quantities. Four-velocity and proper time, four-acceleration. Four-momentum. Lagrangian and Hamiltonian. Mass-shell relation.