SUMMER SCHOOL
Spacetime Mechanics
| When: | 9-15. July 2017 |
| Where: | Somogysimonyi, Hungary |
| Lecturers: | Tamás Matolcsi (Eötvös Loránd University, Budapest) |
| Tamás Fülöp (Budapest University of Technology and Economics) | |
| András László (Wigner Research Centre for Physics) | |
| Áron Szabó (University of Hamburg) | |
| Péter Ván (Wigner Research Centre for Physics) | |
| Cost: | 31000 HUF |
| Language: | Hungarian |
| Lecture notes: | printed lecture notes (in Hungarian) |
Please transfer the fee to: ETTE (Egyesület a Tudomány és a Technika Egységéért), BIC/SWIFT: GIBAHUHBXXX, IBAN: HU75 1160 0006 0000 0000 1980 1517.
Concept
The idea of this summer school is to show the participants a mathematically rigorous and physically sound theory of classical mechanics in a setting that is independent of reference frames, and some applications.
Schedule
Two 90-minute lectures in the morning and in the afternoon; exercise class in the evening. Excursion.
Tematics
- Nonrelativistic spacetime – an overview from the last summer school. World lines. Observers (congruences), splitting. Motion. Vector fields, covector fields, derivatives, spacelike derivative, u-timelike derivative, exterior derivative.
- Absolute Newtonian equationon spacetime. Force fields, potentials, absolute scalar potential.
- Evolution space, absolute and relative physical quantities. The usual Lagrangian and Hamiltonian formalism. Absolute Lagrangian, presymplectic form.
- Spin in classical mechanics. Simultaneous Cartesian product. Action-reaction. Indistinguishable particles.
- Processes, conserved quantities. Process space. The stochastic point of view: Schrödinger and Heisenberg picture in classical mechanics, events, states.
- Group theory: orthogonal groups, Galilean group, Noether group and their notable subgroups. Representations and symmetries. The role of the Lagrangian and the presymplectic form. Classification of irreducible representations of the Noether group, analogies with quantum mechanics.
- An overview of the special relativistic spacetime model. Newtonian equation. Absolute presymplectic form, the absence of an absolute Lagrangian form. No action-reaction and no simulateneous Cartesian product. Relativistic spin, Dirac's equation.
Preliminary literature
Tamás Matolcsi, Spacetime Without Reference Frames, Akadémiai Kiadó, Budapest, 1993
Responsible organisations
MTA WIGNER Research Centre for Physics, Society for the Unity of Science and Technology.
