10–plectic formulation of gravity and Cartan connections
Abstract
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.
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