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 as a product of separate wave functions and represent a pure quantum state. This proposal seems to lead to a mechanism describing the effects of wormholes by which the probability for the scale of wormholes is overwhelmingly concentrated at very small values.