Presymplectic manifolds and the Dirac–Bergmann theory of constraints

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Abstract
We present an algorithm which enables us to state necessary and sufficient conditions for the solvability of generalized Hamilton‐type equations of the form ι (X) ω=α on a presymplectic manifold (M,ω) where α is a closed 1‐form. The algorithm is phrased in the context of global infinite‐dimensional symplectic geometry, and generalizes as well as improves upon the local Dirac–Bergmann theory of constraints. The relation between our algorithm and the geometric constraint theory of Śniatycki, Tulczyjew, and Lichnerowicz is discussed.

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