Advances in Theoretical and Mathematical Physics

Volume 16 (2012)

Number 3

Diffeomorphism-invariant covariant Hamiltonians of a pseudo-Riemannian metric and a linear connection

Pages: 851 – 886



Masqué Jaime Muñoz (Instituto de Física Aplicada, CSIC, Madrid, Spain)

María Eugenia Rosado María (Departamento de Matemática Aplicada, Escuela Técnica Superior de Arquitectura, UPM, Madrid, Spain)


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

Published 7 February 2013