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Presymplectic structures and intrinsic Lagrangians | | Maxim Grigoriev
; | | Date: |
24 Jun 2016 | | Abstract: | It is well-known that a Lagrangian induces a compatible presymplectic form on
the equation manifold (stationary surface, understood as a submanifold of the
respective jet-space). Given an equation manifold and a compatible
presymplectic form therein, we define the first-order 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 first-order 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. | | Source: | arXiv, 1606.7532 | | Services: | Forum | Review | PDF | Favorites | |
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