Polynomial Hamiltonian form of general relativity

Invariant Hamiltonian Quantization of General Relativity

The quantization of General Relativity invariant with respect to time-reparametrizations is considered. We construct the Faddeev-Popov generating functional for the unitary perturbation theory in terms of invariants of the kinemetric group of diffeomorphisms of a frame of reference as a set of Einstein’s observers with the equivalent Hamiltonian description (t = t(t), x = x(t, x, x, x)). The al...

The classical limit and the form of the hamiltonian constraint in non-perturbative quantum general relativity

It is argued that some approaches to non-perturbative quantum general relativity lack a sensible continuum limit that reproduces general relativity. This may be true in spite of their being mathematically well defined diffeomorphism invariant quantum field theories that result from applying canonical quantization to general relativity. The basic problem is that generic physical states lack long...

3 + 1 General Relativity In Hyperbolic Form

Hamiltonian quantization of general relativity with the change of signature.

We show in this article how the usual hamiltonian formalism of General Relativity should be modified in order to allow the inclusion of the Euclidean classical solutions of Einstein’s equations. We study the effect that the dynamical change of signature has on the superspace and we prove that it induces a passage of the signature of the supermetric from (−+++++) to (+−−−−−). Next, all these fea...

Real-polynomial formulation of general relativity in terms of connections.

I show in this letter that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real SO(3) connections. The constraints are simple polynomials in the basic variables. The present framework gives us a new formulation of General Relativity that keeps some of the interesting features of the Ashtekar formulation without the complications associated...