Unit GEOMETRIC METHODS IN THE THEORY OF RELATIVITY
- Course
- Mathematics
- Study-unit Code
- 55A00094
- Curriculum
- Didattico
- Teacher
- Marco Mamone Capria
- Teachers
-
- Marco Mamone Capria
- Hours
- 42 ore - Marco Mamone Capria
- CFU
- 6
- Course Regulation
- Coorte 2025
- Offered
- 2026/27
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Sector
- 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 pseudo-Euclidean geometry, and of differential 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 are in crucial help in clarifying 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. M. Mamone Capria, “The principle of relativity in Newton's Principia and in today's classical physics”, Journal for Foundations and Application of Physics, 2026. B. O'Neill, Semi-Riemannian Geometry, With Applications to Relativity, Academic Press, 1983.
- Educational objectives
- 1) a rigorous understanding of special relativity, as compared to classical physics, and to some aspects of general relativity and cosmology;
2) getting acquainted with the notion of space-time, including a working knowledge of space-time diagrams;
3) an introduction to the historical and theoretical 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 basic differential geometry. Elements of classical physics.
- Teaching methods
- Classes. Office hours. Lecture notes.
- Other information
- Please check the office hours at the web-site http://www.dmi.unipg.it/mamone/, or just contact the teacher to arrange a meeting.
Also, if you plan or are in doubt whether to follow the course, please write to marco.mamonecapria@unipg.it. - Learning verification modality
- Oral examination (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 number of questions on the rest of the program. - 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 spacetime.
Optics and electromagnetism. 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. Teaching special relativity in high school.
Elements of general relativity and cosmology. - Obiettivi Agenda 2030 per lo sviluppo sostenibile
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