MECCANICA SUPERIORE [Higher Mechanics]

Academic Year  2011/12

“Laurea Magistrale in Matematica - Regolamento 2011”

Number of Credits: 6 CFU – Teaching Hours: 42 - “Settore Scientifico Disciplinare”: MAT/07 –

Semester: 1st

Teacher: Marco Mamone Capria – Dipartimento di Matematica e Informatica - Telefono: 075 585 5006 – E-mail: mamone@dmi.unipg.it

Background: Basic concepts of linear algebra and multivariate calculus. Elements of classical physics.

Program: The principle of relativity in classical physics. Newtonian space-time. The origins of special relativity. Derivations of the Lorentz transformations. Affine pseudo-Euclidean geometry. The Poincaré group and its subgroups. Minkowski space-time. Proper time. Relativistic dynamics. Collisions. Mass-energy equivalence. Relativistic electromagnetism. Special relativity and quantum mechanics: some remarks.

Aims: The main objectives of the course are:

1) a rigorous understanding of spacial relativity, as compared to classical physics and to some aspects of quantum mechanics;

2) getting acquainted with the notion of space-time, including a working knowledge of space-time diagrams, both for their rimportance in physics and as a valuable example of applied 4-dimensional geometry;

3) an introduction to the historical issues related to such a momentous change in the foundations of physics as that occurred with the relativity revolution.

Texts/References

R. D’Inverno, Introducing Einstein’s Relativity, Cambridge University Press, 1992

M. Mamone Capria (ed.), Physics Before and After Einstein, IOS, 2005.

A. Sudbery, Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians, Cambridge University Press, 1986.

V. A. Ugarov, Teoria della relatività ristretta, Mir, 1982.

Teaching methods: Classes -- Office hours -- Lecture notes.

Examination: Oral.

Strumenti a supporto della didattica: Saranno distribuite dispense a cura del docente.

Language: Italian

Link: http://www.dmi.unipg.it/mamone/

Office hours: Please check it at the web-site http://www.dmi.unipg.it/mamone/, or just contact me to arrange a meeting.