From multisymplectic to symplectic and back
par Marc Lachièze-Rey
(CNRS, APC)
7 décembre 2016,
14:00
salle Juan Gris, 734A
Université 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.
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