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11 votes

are there natural examples of classical mechanics that happens on a symplectic manifold that...

I think from the physical point of view, the question should be reversed. Symplectic and presymplectic manifolds naturally occur in physics because such geometric structures naturally follow from a va …
Igor Khavkine's user avatar
2 votes
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Infinitesimal generators and conserved quantities (Schrodinger type evolution)

Perhaps part of your question could be phrased as follows. Does there exists a (formally defined) functional $S_1[\psi,\bar{\psi}] = \int dt\,dx\, L_1[\psi,\bar{\psi}]$ such that its Euler-Lagrange de …
Igor Khavkine's user avatar