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arXiv · 1104.2710

Diffeomorphism-invariant Covariant Hamiltonians of a pseudo-Riemannian Metric and a Linear Connection

J. Muñoz Masqué·M. Eugenia Rosado María
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Abstract

\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 $γ$ belonging to this class and every $\mathrm{Diff}N$-invariant Lagrangian density $Λ$ on $J^1(M\times_NC)$, the corresponding covariant Hamiltonian $Λ^γ$ 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.

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J. Muñoz Masqué, M. Eugenia Rosado María. 2011-04-14. Diffeomorphism-invariant Covariant Hamiltonians of a pseudo-Riemannian Metric and a Linear Connection. https://arxiv.org/abs/1104.2710

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