Study-unit Code
In all curricula
Filippo Camilloni
  • Filippo Camilloni
  • 42 ore - Filippo Camilloni
Course Regulation
Coorte 2021
Learning activities
Attività formative affini o integrative
Academic discipline
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Special Relativity. Relativistic kinematics and dynamics. Classical electrodynamics
Reference texts
V. Barone, Relatività, Principi e Applicazioni, Bollati Boringhieri (2011)
Educational objectives
The course represents the first introduction to the Special Relativity together with the description of the classic electrodynamics.

The goal will be the achievement of useful abilities to solve problems within Special Relativity and to approach the solutions of the Maxwell’s equations in peculiar given conditions.

The main knowledge acquired will be:

- Special Relativity principles
- Lorentz’s transformations and their consequences.
- Examples of experiments which confirm the validity of the Special Relativity.
- Introduction to relativistic dynamics.
- The motion of particles in electromagnetic fields.
- Exact solutions to the Maxwell’s equations for given currents.
- Green method for the solution to differential equations.
- Relativistic treatments of particle scattering.

The main skills are:

- the capability to menage the tensor algebra in the Minkowski’s space-time
- the capability to solve problems within relativistic kinematics and dynamics
- the capability to solve Maxwell’s equations in a given gauge with give currents
In order to deal with the main subjects of the course, the student must:

- have a good knowledge of the “Fisica 1” course and the Newtonian mechanics
- have a good knowledge of the electromagnetism course and the Maxwell’s equations
Teaching methods
Direct lectures and exercises.
Other information
Exercises in classrooms and in the teacher's office.
Learning verification modality
There is an oral examination. The discussion will take 30-40 minutes. The questions will cover the full program and exercises will be requested. The examination will test the knowledge and the learning of the student about the course. The examination will also test the student’s capability to communicate with the proper language.

For information about student’s support for students with DSA see:
Extended program
Newtonian mechanics invariance for Galilei’s transformations. Not invariance of the Maxwell’s equations. Ether, star aberration, Michelson-Morley experiment. Length contraction. Lorentz’s transformations for reference systems moving along one axes and parallel axes.
Generalization of Lorentz’s transformations for a generic speed. New composition law for the speed. Relativistic star aberration. Relativistic Doppler’s effect for the electromagnetic radiation. Longitudinal and transverse Doppler’s effects. Casually connected events. Distance separation between events and its invariance under Lorentz’s transformation. Space, time and light like events. Minkowski’s diagrams, light cone, future, past and absolute elsewhere of a given event. Minkowski’s diagrams from different inertial frames. Relativity of simultaneous events, length contraction and time dilation with Minkowski’s diagram. Minkowski’s space-time. Euclidean spaces, metric definition and Riemann’s geometry. Not euclidean spaces and Gauss curvature. Rotations in euclidean space. Pseudo-euclidean spaces. Relativistic dynamics. Four-vectors, four-tensors in Minkowski’s space-time. Lorentz’s transformations as pseudo-orthogonal transformations in Minkowski’s space-time. Inner products and Lorentz’s invariants. Covariant formulation of the dynamics. Proper time, four-speed and four acceleration. Minkowski’s four force. Kinetic energy theorem. E = mc^2, energy of a particle at rest and relativistic energy. Applications of E =mc^2, chemical reactions, fission, and emitted energy from the Sun. Applications of relativistic dynamics, parallel, orthogonal acceleration and inertial mass. The four-momentum and its conservation. Examples of relativistic dynamics. Constant force and initial speed zero. Motion of a charge particle inside a constant electromagnetic field. Relativistic harmonic oscillator period.
Maxwell’s equations. Covariant formulation of the electromagnetism. Field strength tensor. Four density current. Lorentz’s transformations for the four density current. Four potential and solution to the Bianchi’s identity in empty space. Gauge invariance. Lorentz and Coulomb’s gauges. Solution of the Poisson’s equation in terms of Green’s functions. Fourier’s transforms and Green’s functions. Laplacian’s Green functions. Solution to the the equation for the vector potential in Coulomb’s gauge. Covariant formulation of connection equations. Maxwell’s equations and their solutions for slow particles in external fields. Four force density. Energy-momentum tensor. Conservation theorems. Relativistic lagrangian and hamiltonian of a free particle and of a particle within an external electromagnetic field.
Peculiar solution of the Maxwell’s equation with external currents in the Lorentz gauge. Dalambertian Green’s function. Delayed potentials. Lienard-wiechert potentials. Larmor's formulas. Plane wave solution to the Maxwell's equations without sources. Lagrangian for the vector potential.
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