Quantum scalar field in quantum gravity: the propagator and Lorentz invariance in the spherically symmetric case

We recently studied gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since there are local degrees of freedom one faces the "problem of dynamics". We attack it using the "uniform discretization technique". We find the quantum state that minimizes the value of the master constraint for the case of weak fields and curvatures. The state has the form of a direct product of Gaussians for the gravitational variables times a modified Fock state for the scalar field. In this paper we do three things. First, we verify that the previous state also yields a small value of the master constraint when one polymerizes the scalar field in addition to the gravitational variables. We then study the propagators for the polymerized scalar field in flat space-time using the previously considered ground state in the low energy limit. We discuss the issue of the Lorentz invariance of the whole approach. We note that if one uses real clocks to describe the system, Lorentz invariance violations are small. We discuss the implications of these results in the light of Horava's Gravity at the Lifshitz point and of the argument about potential large Lorentz violations in interacting field theories of Collins et. al.Comment: Dedicated to Josh Goldberg, to appear in special issue of Gen. Rel. Grav., 14 pages RevTex. We expanded the section on Lorentz invarianc

New variables for 1+1 dimensional gravity

We show that the canonical formulation of a generic action for 1+1-dimensional models of gravity coupled to matter admits a description in terms of Ashtekar-type variables. This includes the CGHS model and spherically symmetric reductions of 3+1 gravity as particular cases. This opens the possibility of discussing models of black hole evaporation using loop representation techniques and verifying which paradigm emerges for the possible elimination of the black hole singularity and the issue of information loss.Comment: 8 pages, no figures, added references, corrected some misleading statement

Gravitation in terms of observables 2: the algebra of fundamental observables

In a previous paper, we showed how to use the techniques of the group of loops to formulate the loop approach to gravity proposed by Mandelstam in the 1960's. Those techniques allow to overcome some of the difficulties that had been encountered in the earlier treatment. In this approach, gravity is formulated entirely in terms of Dirac observables without constraints, opening attractive new possibilities for quantization. In this paper we discuss the Poisson algebra of the resulting Dirac observables, associated with the intrinsic components of the Riemann tensor. This provides an explicit realization of the non-local algebra of observables for gravity that several authors have conjectured.Comment: 21 pages, RevTex, 4 figure