Seminár z teoretickej fyziky - Marián Fecko (5.3.2019)
v utorok 5.3.2019 o 14:00 hod. v miestnosti F2/125
Od: Peter Maták
Prednášajúci: Marián Fecko
Názov: 100 years (plus epsilon) of Noether theorem
Termín: 5.3.2019, 14:00 hod., F2/125
In July 1918, Emmy Noether published her seminal paper ,,Invariante Variationsprobleme''. It contains a theorem describing how symmetries (of a variational problem) are related to conserved quantities.
Since equations of motion in physics are closely related to variational problems (via the extremal action principle), the theorem is a folklore knowledge in theoretical physics, its versions may be found in virtually any textbook on theoretical mechanics or quantum field theory. Because of its importance for physics as well as the fact, that we forgot to pay due tribute to it in 2018, we try to do it just now.
After brief description of the historical context and (as well brief) sketch of the traditional (coordinate) look of the theorem, our presentation focuses on its present status. In particular, we try to show, using deep insight of P.Ševera, how simple the result may become when one looks at the problem from ,,right'' perspective, i.e. using simple modern differential geometry and ignoring obscuring details. The exposition also prepares material for a possible next talk on how (naturally) Lie and Courant algebroids enter the scene in variational problems with symmetries.