
Course unit
FUNDAMENTS OF RELATIVITY
SCM0014353, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/05 
Astronomy and Astrophysics 
4.0 
Core courses 
FIS/02 
Theoretical Physics, Mathematical Models and Methods 
6.0 
Course unit organization
Period 
First semester 
Year 
3rd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
10.0 
80 
170.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
6 Commissione Istituzioni di relatività 20182019 
01/10/2018 
30/11/2019 
MARTUCCI
LUCA
(Presidente)
DALL'AGATA
GIANGUIDO
(Membro Effettivo)
GIUSTO
STEFANO
(Supplente)

Prerequisites:

Calculus 1, 2, and 3. Physics 1 and 2. Geometry. Analytical Mechanics. 
Target skills and knowledge:

Relativity: Understanding the foundations of Special Relativity. Ability to solve elementary problems in relativistic mechanics. Ability to use tensor calculus.
Mathematical methods: Basic knowledge of distributions, Fourier transforms, tensor calculus. 
Examination methods:

Relativity: Written exam with exercises and oral exam with questions about the course topics.
Mathematical methods: Mandatory written exam with exercises and optional oral exam with questions about the course topics. 
Assessment criteria:

Knowledge and understanding of the course topics, ability in the solution of elementary problems related to the course topics. 
Course unit contents:

Relativity:
1) Symmetries and invariances. Intertial frames, physical laws, Galilean group. Simultaneity and Newtonian measurements. Speed of light, the aether. Experimental evidences of the finiteness and constance of the speed of light.
2) The new mechanics: the principle of relativity. Postulates of special relativity. Minkowski diagrams. Worldline. Simultaneity. Lorentz transformations.
3) Relativistic kinematics  basics: The interval, the Minkowski metric. Matrix representation of Lorentz transformations. Rapidity. Composition of velocities. Time dilation. Lengths contraction. PenroseTerrell rotation. The twin paradox.
4) Covariant Relativistic kinematics: Poincaré and Lorentz symmetry groups. Covariant formalism. Tensors. Relativistic momentum. Kinetic energy, rest energy and energymass equivalence.
5) Relativistic kinematics  optics: Angle transformations; Stellar aberration. Relativistic Doppler effect.
6) Scattering: Momentum conservation. Particle dacays. Threshold energy. Invariant mass.
7) Electromagnetism: 4potential and covariant formulation of Maxwell's equations. Gauge invariance. Lorentz transformations of the electromagnetic field. Relativistic invariants. Maxwell equations in vacuo. Solution of the wave equations and its properties. Continuity law for electric currents. Motion of charges in constant electric and magnetic fields.
8) Introduction to General Relativity: The equivalence principle. The metric. Inertial and gravitational forces. Accelerated observers. Rindler spacetime. Time dilation.
Mathematical Methods:
1) Tensors and special relativity: Rotations in euclidean space. Minkowski space, Lorentz and Poincaré transformations. Proper ortochronous transformations. Covariant and contravariant basis. Scalar fields, vector and tensor fields. Divergence and continuity equation in covariant form. Symmetry and Antisymmetry of indices. Differential forms. Exterior derivative. Invariant (Pseudo)tensors: Kronecker delta, metric, LeviCivita pseudotensor. Tensor products and contractions.
2) Distributions: General motivations. Test functions and S(R) space. Regular and singular tempered distributions. Examples: Dirac delta and principal value. Weak convergence. Approximation of singular distributions by means of regular ones. Operations on distributions: derivative, complex conjugation, rescaling and shift of a variable. Dirac delta of a function. Fourier transform and Fourier theorem in S(R). Convolution of functions and their properties. Convolution theorem. Symmetry and reality. Parseval formula. Fourier transform of distributions and Fourier theorem for distributions. Applications: Fourier transform of the Dirac delta function, of a constant function, of the sign function, of the stepfunction. Convolutions of distributions and their properties. 
Planned learning activities and teaching methods:

Lectures and individual and group activities. Lectures are given in Italian. 
Additional notes about suggested reading:

Suggested textbooks. Exercises on the course topics are available through the website of the course on the elearning platform of the Department of Physics and Astronomy "G. Galilei" (https://elearning.unipd.it/dfa/). 
Textbooks (and optional supplementary readings) 

Gasperini, Maurizio, Manuale di relatività ristretta per la laurea triennale in fisica. Milano: Springer, 2010.

Barone, Vincenzo, Relatività, principi e applicazioni. Torino: Bollati Boringhieri, 2004.

Rindler, Wolfgang, Relativity: Special, general, and cosmological. Oxford: Oxford University Press, 2016.

Innovative teaching methods: Teaching and learning strategies
 Case study
 Working in group
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)

