10-plectic formulation of gravity and Cartan connections

Abstract: We give a Hamiltonian formulation of %the first order 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.