Unconstrained Hamiltonian formulation of general relativity with thermo-elastic sources

Unconstrained Hamiltonian Formulation of SU(2) Gluodynamics

One of the main issues in the Hamiltonian formulation of Yang-Mills theories is to find the projection from the phase space of canonical variables constrained by the non-Abelian Gauss law to the “smaller” phase space of unconstrained gauge invariant coordinates only. Dealing with the problem of the elimination of the pure gauge degrees of freedom two approaches exist, the perturbative and the n...

Lagrangian Formulation of General Relativity

Hyperbolic Formulation of General Relativity

Einstein’s theory, viewed mathematically as a system of second-order partial differential equations for the metric, is not a hyperbolic system without modification and is not manifestly well-posed, though physical information propagates at the speed of light. A well-posed hyperbolic system admits unique solutions which depend continuously on the initial data and seems to be required for robust,...

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...

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...