10-plectic formulation of gravity and Cartan connections

TL;DR

This paper develops a Hamiltonian formulation of Cartan gravity within a 10-plectic geometric framework, revealing that local equivariance of the Cartan connection follows from the Hamiltonian equations.

Contribution

It introduces a covariant Hamiltonian approach to Weyl--Einstein--Cartan gravity using 10-plectic geometry, linking Cartan connection properties to Hamiltonian dynamics.

Findings

Cartan connection's local equivariance arises from Hamilton equations

Formulation is covariant within principal fiber bundle geometry

Establishes a 10-plectic framework for gravity theories

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 Poincar\'{e} 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.