Zákony zachování v moderních variačních teoriích. Odkaz Emmy Noetherové
| Title in English | Conservation laws in modern variational theories. The heritage of Emmy Noether |
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| Authors | |
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Československý časopis pro fyziku |
| MU Faculty or unit | |
| Citation | |
| Field | Theoretical physics |
| Keywords | variational principle; conservation law; fibered manifolds; differential forms |
| Description | The question of the origin of conservation laws for the momentum, angular momentum, mechanical energy and other quantities in classical mechanics and classical field theories can be answered by various ways. Nevertheless, in principle the conserved quantities are connected with the symmetry of a problem under consideration. For variational theories such a connection was disclosed by the Emmy Noether theorem derived in 1918 by a classical “coordinate” procedure using variations, which was typical for the former calculus of variations. The elaborate modern geometrical formalism of fibred manifolds and differential forms adapted to their fibred structure is a much more effective tool not only for variational theories themselves but also for their consequences as the Noether theorem. The merit of the geometrical approach can be explained by the simplest example – a one-dimensional motion of a classical mechanical particle. |
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