10–plectic formulation of gravity and Cartan connections

Dimitri Vey (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We give a Hamiltonian formulation of Weyl–Einstein–Cartan gravity which is covariant from the viewpoint of the geometry of the principal fiber bundle. The connection is represented by a 1-form with values in the Poincaré Lie algebra, which is defined on the total space of the orthonormal frame bundle fibered over the space-time. Within the 10-plectic framework we discover that the local equivariance property of the Cartan connection is a consequence of the Hamilton equations.

Mots clés: General Relativity; FIrst order gravity; Cartan connections; Multisymplectic Geometry

Domaines: Mathématiques [math]; Physique [physics]

Dimitri Vey. 10–plectic formulation of gravity and Cartan connections. 2016. ⟨hal-01408289v1⟩