Hamiltonian lattice gravity. II. Discrete moving-frame formulation

Is Barbero’s Hamiltonian formulation a Gauge Theory of Lorentzian Gravity?

This letter is a critique of Barbero’s constrained Hamiltonian formulation of General Relativity on which current work in Loop Quantum Gravity is based. We show that if one tries to interpret Barbero’s real SO(3) connection as a space–time gauge field, the theory is not diffeomorphism invariant. In this respect, Barbero’s connection is quite different from Ashtekar’s, which does admit a space–t...

Discrete Moving Frames on Lattice Varieties and Lattice-Based Multispaces

In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame defined on a lattice variety, and the equivalence classes of global syzygies that result from the first fundamental group of the variety. In the second half, we consider the continuum limit of discrete moving frames as a local lattice coale...

Hamiltonian spinfoam gravity

Torsion formulation of gravity

We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.

Isominkowskian Formulation of Gravity

We submit the viewpoint that, perhaps, some of the controversies in gravitation occurred during this century are not due to insufficiencies of Einstein’s field equations, but rather to insufficiencies in the mathematics used for their treatment. For this purpose we treat the same equations with the novel, broader isomathematics and related isominkowskian geometry, and show an apparently final r...