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Detailed Programme of the Week 09/28/2020 -- 10/02/2020:
-- Introduction and Special Relativity
LECT 1 -- Monday
09/28/2020 - 2h Bonciani 12:00-14:00
(Majorana) meet.google.com/rkn-mafj-mra
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 09/29/2020 - 2h
Bonciani 8:00-10:00 (Conversi)
meet.google.com/szf-gndu-pwc
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 .
Boost in the x direction. General case. Limit of small velocity
and the recovery of Galilean transformations.
LECT 3 -- Wednesday 09/30/2020 - 2h Bonciani
9:00-11:00 (Conversi) meet.google.com/szf-gndu-pwc
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. 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
. metric tensor.
Contravariant and covariant vectors in
.
LECT 4 -- Thursday 10/01/2020 - 2h Bonciani
8:00-10:00 (Majorana) meet.google.com/rkn-mafj-mra
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. Lorentz
transformations form a Group. Structure of the group.
Poincare' Group.
LECT 5 -- Friday 10/02/2020 - 2h Bonciani
8:00-10:00 (Conversi) meet.google.com/szf-gndu-pwc
Infinitesimal transformations. Lagrangian
and Hamiltonian mechanics. The free particle. Least Action
Principle. Lagrangian and Relativity. Relativistic free particle.
Euler-Lagrange equations. Conservation laws. Lagrangian invariant
under Poincare' transformation and conservation of the
four-momentum and angular momentum.