%0 Journal Article
%T Diffeomorphism-invariant Covariant Hamiltonians of a pseudo-Riemannian Metric and a Linear Connection
%A J. Mu£¿oz Masqu¨¦
%A M. Eugenia Rosado Mar¨ªa
%J Physics
%D 2011
%I arXiv
%X \noindent Let $M\to N$ (resp.\ $C\to N$) be the fibre bundle of pseudo-Riemannian metrics of a given signature (resp.\ the bundle of linear connections) on an orientable connected manifold $N$. A geometrically defined class of first-order Ehresmann connections on the product fibre bundle $M\times_NC$ is determined such that, for every connection $\gamma $ belonging to this class and every $\mathrm{Diff}N$-invariant Lagrangian density $\Lambda $ on $J^1(M\times_NC)$, the corresponding covariant Hamiltonian $\Lambda ^\gamma $ is also $\mathrm{Diff}N$-invariant. The case of $\mathrm{Diff}N$-invariant second-order Lagrangian densities on $J^2M$ is also studied and the results obtained are then applied to Palatini and Einstein-Hilbert Lagrangians.
%U http://arxiv.org/abs/1104.2710v1