Unit GEOMETRIC METHODS IN THE THEORY OF RELATIVITY
- Course
- Mathematics
- Study-unit Code
- 55A00094
- Curriculum
- Didattico-generale
- Teacher
- Marco Mamone Capria
- Teachers
-
- Marco Mamone Capria
- Hours
- 42 ore - Marco Mamone Capria
- CFU
- 6
- Course Regulation
- Coorte 2022
- Offered
- 2022/23
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/03
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The theory of relativity as an application of the pseudo-Euclidean geometry, of differential topology and geometry and group theory to physics. The treatment pays attention to the historical and critical development of formalism and theories, and stresses how mathematical tools help to clarify conceptual issues.
- Reference texts
- R. D’Inverno, Introducing Einstein’s Relativity, Cambridge University Press, 1992
M. Mamone Capria (a cura di), Physics Before and After Einstein, IOS, 2005.
B. O'Neill, Semi-Riemannian Geometry, With Applications to Relativity, Academic Press, 1983
A. Sudbery, Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians, Cambridge University Press, 1986.
Lecture notes by the teacher. - Educational objectives
- The main objectives of the course are:
1) a rigorous understanding of spatial relativity, as compared to classical physics and to some aspects of quantum mechanics and general relativity;
2) introducing the cosmological problem in its relationship with the evolution oif the concept of geometric space;
3) getting acquainted with the different concepts of space-time, including a working knowledge of space-time diagrams, both for their importance in physics and as a valuable example of applied 4-dimensional geometry;
4) an introduction to the historical issues concerning such momentous changes in the foundations of physics as that occurred with the relativity revolution.
The course is also suitable for would-be high-school mathematics and physics teachers. - Prerequisites
- A working knowledge of basic linear algebra, multivariate calculus, and differential geometry. Elements of classical physics.
The course is thoroughly presented in a user-friendly fashion. - Teaching methods
- Classes -- Office hours -- Lecture notes.
- Other information
- Please check the office hours at the web-site https://mamonecapria.sites.dmi.unipg.it/, or just contact the teacher to arrange a meeting.
- Learning verification modality
- Oral examination of about 45-60 minutes (in any language previously agreed upon with the teacher), including some simple written problems. The examination starts with an in-depth
treatment on a topic selected by the student from the program, followed by a few basic questions on the rest of the program.
Students with disability may wish to consult http://www.unipg.it/disabilita-e-dsa. - Extended program
- General outline of the foundations of physics in its historical and critical development. The universe from a topological and geometrical point of view. 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. About the pedagogy of special relativity for high school. Relationship of special relativity and quantum mechanics. Relativistic electromagnetism. An outline of standard cosmological relativity.