Long range correlations in quantum gravity

Abstract

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. Thiemann's 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 $\pm$ 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.

29 pages; LaTex; 9 figures in .eps files

References in corpus (4)

• ``Sum over Surfaces'' form of Loop Quantum Gravity
• Causal evolution of spin networks
• Matrix Elements of Thiemann's Hamiltonian Constraint in Loop Quantum Gravity
• The classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity

Cited by in corpus (5)

• Loop quantum gravity: an outside view
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Loop and spin foam quantum gravity: a brief guide for beginners
• The volume operator for spin networks with planar or cylindrical symmetry
• Minisuperspace models of discrete systems