The density matrix of wormholes

The quantum state of wormholes has been described by a wave function which is a functional of the metric and matter field configurations on a three-sphere S which divides the space-time four-manifold M into two disconnected parts. We present here the alternate proposal that the quantum state of a single wormhole should be described by a non-factorizable density matrix representing a mixed state, rather than a pure state. Such a density matrix would not contain any isolable part which could be given a product of separate wave functions and represent a pure quantum state. This proposal seems to lead to mechanism describing the effects of wormholes by which the probability for the scale of wormholes is overwhelmingly concentrated at very small values. (orig.)