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Accueil > Archives > Anciens projets de recherche financés > Projet ERC Philosophie de la Gravitation Quantique Canonique > Evénements > Talk : Marc Lachièze-Rey

Talk : Marc Lachièze-Rey

From multisymplectic to symplectic and back

by Marc Lachièze-Rey

December 7, 2016,
Room Juan Gris, 734A

University Paris Diderot

In (classical) field theories, it is often considered that one must choose between symplectic structure and covariance. The latter is maintained, e.g., by a multisymplectic formalism. I express dynamics in terms of histories, which means considering not the phase space itself, but the space of sections on the phase space bundle. I show that it is possible to develop a "historical" dynamics, entirely covariant, where one may define a (generalized) symplectic form. The equations of motion and the conservation laws are easily derived and take a very simple and general form. One recovers the multisymplectic formalism by projection onto phase space ; and also the usual symplectic form on the space of solutions (Souriau, Crnkovic and Witten). I claim that this is a very natural approach of mechanics.

Room Malevitch, 483A, building Condorcet,
4, rue Elsa Morante, 75013 Paris.
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