Regularization of the Hamiltonian constraint and the closure of the constraint algebra

In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An important issue considered in the paper is the closure of the constraint algebra. The main result we obtain is that the Poisson bracket between the regulated Hamiltonian constraint and the Diffeomorphism constraint is equal to a sum of regulated Hamiltonian constraints with appropriately redefined regulating functions.Comment: 23 pages, epsfig.st

Graphical Evolution of Spin Network States

The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution, and evaluate its action both on edges and on vertices of the spin network states. The analytical computations are carried out completely to yield a finite, diffeomorphism invariant result. We use techniques from the recoupling theory of colored graphs with trivalent vertices to evaluate the graphical part of the Hamiltonian action. We show that the action on edges is equivalent to a diffeomorphism transformation, while the action on vertices adds new edges and re-routes the loops through the vertices.Comment: 24 pages, 21 PostScript figures, uses epsfig.sty, Minor corrections in the final formula in the main body of the paper and in the formula for the Tetrahedral net in the Appendi

Quantum causal histories

Quantum causal histories are defined to be causal sets with Hilbert spaces attached to each event and local unitary evolution operators. The reflexivity, antisymmetry, and transitivity properties of a causal set are preserved in the quantum history as conditions on the evolution operators. A quantum causal history in which transitivity holds can be treated as ``directed'' topological quantum field theory. Two examples of such histories are described.Comment: 16 pages, epsfig latex. Some clarifications, minor corrections and references added. Version to appear in Classical and Quantum Gravit

Causality in Spin Foam Models

We compute Teitelboim's causal propagator in the context of canonical loop quantum gravity. For the Lorentzian signature, we find that the resultant power series can be expressed as a sum over branched, colored two-surfaces with an intrinsic causal structure. This leads us to define a general structure which we call a ``causal spin foam''. We also demonstrate that the causal evolution models for spin networks fall in the general class of causal spin foams.Comment: 19 pages, LaTeX2e, many eps figure

Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra

In a companion paper we introduced a kinematical arena for the discussion of the constraints of canonical quantum gravity in the spin network representation based on Vassiliev invariants. In this paper we introduce the Hamiltonian constraint, extend the space of states to non-diffeomorphism invariant ``habitats'' and check that the off-shell quantum constraint commutator algebra reproduces the classical Poisson algebra of constraints of general relativity without anomalies. One can therefore consider the resulting set of constraints and space of states as a consistent theory of canonical quantum gravity.Comment: 20 Pages, RevTex, many figures included with psfi

Closed-Flux Solutions to the Constraints for Plane Gravity Waves

The metric for plane gravitational waves is quantized within the Hamiltonian framework, using a Dirac constraint quantization and the self-dual field variables proposed by Ashtekar. The z axis (direction of travel of the waves) is taken to be the entire real line rather than the torus (manifold coordinatized by (z,t) is RxR rather than $S_1$ x R). Solutions to the constraints proposed in a previous paper involve open-ended flux lines running along the entire z axis, rather than closed loops of flux; consequently, these solutions are annihilated by the Gauss constraint at interior points of the z axis, but not at the two boundary points. The solutions studied in the present paper are based on closed flux loops and satisfy the Gauss constraint for all z.Comment: 18 pages; LaTe

KMS states on Quantum Grammars

We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself. In physics such evolution was discussed in connection with quantum gravity. It is also related to what is called quantum circuits, one of the incarnations of a quantum computer. We consider simpler models for which one can obtain exact mathematical results. We prove existence of the dynamics in both Schroedinger and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We show (for high temperatures) that for each system where the lattice undergoes quantum evolution, there is a natural scaling leading to a quantum spin system on a fixed lattice, defined by a renormalized Hamiltonian.Comment: 22 page

Production of Polarized Vector Mesons off Nuclei

Using the light-cone QCD dipole formalism we investigate manifestations of color transparency (CT) and coherence length (CL) effects in electroproduction of longitudinally (L) and transversally (T) polarized vector mesons. Motivated by forthcoming data from the HERMES experiment we predict both the A and Q^2 dependence of the L/T- ratios, for rho^0 mesons produced coherently and incoherently off nuclei. For an incoherent reaction the CT and CL effects add up and result in a monotonic A dependence of the L/T-ratio at different values of Q^2. On the contrary, for a coherent process the contraction of the CL with Q^2 causes an effect opposite to that of CT and we expect quite a nontrivial A dependence, especially at Q^2 >> m_V^2.Comment: Revtex 24 pages and 14 figure

Nonstandard optics from quantum spacetime

We study light propagation in the picture of semi-classical space-time that emerges in canonical quantum gravity in the loop representation. In such picture, where space-time exhibits a polymer-like structure at microscales, it is natural to expect departures from the perfect non-dispersiveness of ordinary vacuum. We evaluate these departures, computing the modifications to Maxwell's equations due to quantum gravity, and showing that under certain circumstances, non-vanishing corrections appear that depend on the helicity of propagating waves. These effects could lead to observable cosmological predictions of the discrete nature of quantum spacetime. In particular, recent observations of non-dispersiveness in the spectra of gamma-ray bursts at various energies could be used to constrain the type of semi-classical state that describes the universe.Comment: 4 pages, RevTeX, no figure