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

2011/04/14 by J. Muñoz Masqué, Masqué, J. Muñoz, E. Rosado María +2
Mathematics · Physics and Astronomy · #58J70 #83C05 #Advanced Differential Geometry Research #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Primary: 58E30 #Secondary: 58A20 #math-ph #math.MP #msc:58A20 #msc:58E30 #msc:58J70 #msc:83C05

paper · pdf · doi:10.48550/arxiv.1104.2710

arxiv created 2011/04/14 · openalex publication_date 2011/04/14 · arxiv updated 2011/04/15 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

\noindent Let M→ N (resp. C→ 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×_NC is determined such that, for every connection γ belonging to this class and every DiffN-invariant Lagrangian density Λ on J¹(M×_NC), the corresponding covariant Hamiltonian Λ^γ is also DiffN-invariant. The case of DiffN-invariant second-order Lagrangian densities on J²M is also studied and the results obtained are then applied to Palatini and Einstein-Hilbert Lagrangians.

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