Presymplectic structures and intrinsic Lagrangians
Abstract
It is wellknown that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface, understood as a submanifold of the respective jetspace). Given an equation manifold and a compatible presymplectic form therein, we define the firstorder Lagrangian system which is formulated in terms of the intrinsic geometry of the equation manifold. It has a structure of a presymplectic AKSZ sigma model for which the equation manifold, equipped with the presymplectic form and the horizontal differential, serves as the target space. For a wide class of systems (but not all) we show that if the presymplectic structure originates from a given Lagrangian, the proposed firstorder Lagrangian is equivalent to the initial one and hence the Lagrangian per se can be entirely encoded in terms of the intrinsic geometry of its stationary surface. If the compatible presymplectic structure is generic, the proposed Lagrangian is only a partial one in the sense that its stationary surface contains the initial equation manifold but does not necessarily coincide with it.
 Publication:

arXiv eprints
 Pub Date:
 June 2016
 DOI:
 10.48550/arXiv.1606.07532
 arXiv:
 arXiv:1606.07532
 Bibcode:
 2016arXiv160607532G
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 26 pages