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arXiv · 1509.01037

Second-order Lagrangians admitting a first-order Hamiltonian formalism

E. Rosado María·J. Muñoz Masqué
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Abstract

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) for each second-order Lagrangian density on an arbitrary fibred manifold $p\colon E\to N$ the Poincar\'e-Cartan form of which is projectable onto $J^1E$, by using a new notion of regularity previously introduced, a first-order Hamiltonian formalism is developed for such a class of variational problems; ii) the existence of first-order equivalent Lagrangians are discussed from a local point of view as well as global; iii) this formalism is then applied to classical Einstein-Hilbert Lagrangian and a generalization of the BF theory. The results suggest that the class of problems studied is a natural variational setting for GR.

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E. Rosado María, J. Muñoz Masqué. 2015-09-03. Second-order Lagrangians admitting a first-order Hamiltonian formalism. https://arxiv.org/abs/1509.01037

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