Donald E. Neville

Long range correlations in quantum gravity

Smolin has pointed out that the spin network formulation of quantum gravity will not necessarily possess the long range correlations needed for a proper classical limit; typically, the action of the scalar constraint is too local. Thiemanns length operator is used to argue for a further restriction on the action of the scalar constraint: it should not introduce new edges of color unity into a spin network, but should rather change preexisting edges by

Volume operator for singly polarized gravity waves with planar or cylindrical symmetry

\pm

Total intrinsic spin for plane gravity waves

one unit of color. Smolin has proposed a specific ansatz for a correlated scalar constraint. This ansatz does not introduce color unity edges, but the [scalar, scalar] commutator is shown to be anomalous. In general, it will be hard to avoid anomalies, once correlation is introduced into the constraint; but it is argued that the scalar constraint may not need to be anomaly-free when acting on the kinematic basis.

Closed-flux solutions to the quantum constraints for plane gravity waves

A previous paper constructed a kinematic basis for spin networks with planar or cylindrical symmetry and arbitrary polarization. This paper imposes a constraint which limits the gravitational wave to a single polarization. The spectrum of the constraint contains a physically reasonable number of zero eigenvalues, and the zero eigenvectors can be constructed explicitly. Commutation of the constraint with the Hamiltonian is expected to lead to a further constraint. This new constraint is not investigated in this paper, but I argue it will be nonlocal, relating states at two or more neighboring vertices.0.

Broken-mass solutions to superconvergence relations

A quantity which measures total intrinsic spin along the z axis is constructed for planar gravity (fields dependent on z and t only), in both the Ashtekar complex connection formalism and in geometrodynamics. The total spin is conserved but (surprisingly) is not a surface term. This constant of the motion coincides with one of four observables previously discovered by Husain and Smolin. Two more of those observables can be interpreted physically as raising and lowering operators for total spin.

Gravity Lagrangian with ghost-free curvature-squared terms

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

Gravity theories with propagating torsion

S_1

Experimental Bounds on the Coupling Strength of Torsion Potentials

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.

A Technique for Solving Recurrence Relations Approximately and Its Application to the 3‐J and 6‐J Symbols

We use an ansatz motivated by duality and the quark model to saturate superconvergence relations near t=0 for scattering of mesons in the vector and pseudoscalar nonets. The saturation is carried out with a few low-lying states, using the observed mass spectrum rather than the degenerate masses characteristic of a nonet -- or SU(6) -- symmetric model. (AIP)