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June 2012 Diffeomorphism-invariant covariant Hamiltonians of a pseudo-Riemannian metric and a linear connection
Masqué Jaime Muñoz, María Eugenia Rosado María
Adv. Theor. Math. Phys. 16(3): 851-886 (June 2012).

Abstract

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 $\operatorname{Diff}N$-invariant Lagrangian density $\Lambda $ on $J^1(M\times _NC)$, the corresponding covariant Hamiltonian $\Lambda ^\gamma $ is also $\operatorname{Diff}N$-invariant. The case of $\operatorname{Diff}N$-invariant second-order Lagrangian densities on $J^2M$ is also studied and the results obtained are then applied to Palatini and Einstein-Hilbert Lagrangians.

Citation

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Masqué Jaime Muñoz. María Eugenia Rosado María. "Diffeomorphism-invariant covariant Hamiltonians of a pseudo-Riemannian metric and a linear connection." Adv. Theor. Math. Phys. 16 (3) 851 - 886, June 2012.

Information

Published: June 2012
First available in Project Euclid: 20 March 2013

zbMATH: 1266.53027
MathSciNet: MR3024276

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 3 • June 2012
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