## Advances in Theoretical and Mathematical Physics

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

#### 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.

#### Article information

Source
Adv. Theor. Math. Phys., Volume 16, Number 3 (2012), 851-886.

Dates
First available in Project Euclid: 20 March 2013