Unit SPECIAL RELATIVITY AND ELECTRODYNAMICS
 Course
 Physics
 Studyunit Code
 A001747
 Curriculum
 In all curricula
 Teacher
 Matteo Rinaldi
 Teachers

 Matteo Rinaldi
 Hours
 42 ore  Matteo Rinaldi
 CFU
 6
 Course Regulation
 Coorte 2020
 Offered
 2021/22
 Learning activities
 Affine/integrativa
 Area
 Attività formative affini o integrative
 Academic discipline
 FIS/02
 Type of studyunit
 Obbligatorio (Required)
 Type of learning activities
 Attività formativa monodisciplinare
 Language of instruction
 Italian
 Contents
 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 spacetime
 the capability to solve problems within relativistic kinematics and dynamics
 the capability to solve Maxwell’s equations in a given gauge with give currents  Prerequisites
 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 3040 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:
http://www.unipg.it/disabilitaedsa  Extended program
 Newtonian mechanics invariance for Galilei’s transformations. Not invariance of the Maxwell’s equations. Ether, star aberration, MichelsonMorley 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 spacetime. Euclidean spaces, metric definition and Riemann’s geometry. Not euclidean spaces and Gauss curvature. Rotations in euclidean space. Pseudoeuclidean spaces. Relativistic dynamics. Fourvectors, fourtensors in Minkowski’s spacetime. Lorentz’s transformations as pseudoorthogonal transformations in Minkowski’s spacetime. Inner products and Lorentz’s invariants. Covariant formulation of the dynamics. Proper time, fourspeed 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 fourmomentum 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. Energymomentum 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. Lienardwiechert potentials. Larmor and Lienard’s formulas.