Second-order Lagrangians admitting a first-order Hamiltonian formalism

2015/09/03 by María, E. Rosado, Masqué, J. Muñoz
#58A20 #58E30 #83C05 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1509.01037

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→ N the Poincaré-Cartan form of which is projectable onto J¹E, 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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