SIGNATURE TRANSITIONS IN QUANTUM COSMOLOGY

We exhibit a family of Hilbert subspaces describing solutions to the Wheeler-DeWitt equation. Each subspace describes a distinct quantum theory in which the parameters of the potential are required to satisfy a particular 'quantization' condition. Tentative evidence suggests that within each Hilbert subspace there exist states that may be identified with non-dispersive wave packets peaking in the vicinity of submanifolds in superspace corresponding to classical cosmological eras. These submanifolds admit parametrizations corresponding to metric solutions of Einstein's equations that admit a transition between a Euclidean and a Lorentzian signature.