Abstract
In this paper we argue that the symplectic description of classical mechanics contains many elements of the Lagrange formulation of classical mechanics, in particular a variational description in terms of an action functional. In order to obtain these results, one has to enlarge the symplectic formulation with part of the prequantization construction: the construction of a principal S 1-bundle with connection over the symplectic manifold, but without the quantization condition. We propose to call this enlargement the ‘postclassical formalism.’ Apart from mathematical evidence that the post-classical formalism is a (very) useful enlargement of symplectic mechanics, we also argue that this formalism has physical content.
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Tuynman, G.M. (2003). The Lagrangian in Symplectic Mechanics. In: de Gosson, M. (eds) Jean Leray ’99 Conference Proceedings. Mathematical Physics Studies, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2008-3_17
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DOI: https://doi.org/10.1007/978-94-017-2008-3_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6316-8
Online ISBN: 978-94-017-2008-3
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