Hamiltonian form of Carroll gravity

Hamiltonian spinfoam gravity

Hamiltonian Gravity and Noncommutative Geometry

A version of foliated spacetime is constructed in which the spatial geometry is described as a time dependent noncommutative geometry. The ADM version of the gravitational action is expressed in terms of these variables. It is shown that the vector constraint is obtained without the need for an extraneous shift vector in the action.

Multi-Hamiltonian structure of self-dual gravity

We discover multi-Hamiltonian structure of the complex MongeAmpère equation (CMA) set in a real first-order two-component form. Therefore, by Magri’s theorem this is a completely integrable system in four real dimensions. We start with Lagrangian and Hamiltonian densities in real variables, a symplectic form and the Hamiltonian operator, that determines the Poisson bracket. We have calculated a...

Hamiltonian structure of 2+1 dimensional gravity

A summary is given of some results and perspectives of the hamiltonian ADM approach to 2 + 1 dimensional gravity. After recalling the classical results for closed universes in absence of matter we go over the the case in which matter is present in the form of point spinless particles. Here the maximally slicing gauge proves most effective by relating 2 + 1 dimensional gravity to the RiemannHilb...

Quantum gravity Hamiltonian for manifolds with boundary.

In canonical quantum gravity, when space is a compact manifold with boundary there is a Hamiltonian given by an integral over the boundary. Here we compute the action of this `boundary Hamiltonian' on observables corresponding to open Wilson lines in the new variables formulation of quantum gravity. Up to a divergent factor, it is given by a `shift operator' resembling that in Morales-T ecotl a...