WAVE-FUNCTIONS ON A MINISUPERSPACE OF HIGHER-DIMENSIONAL GEOMETRIES

We consider minisuperspace quantum models of the universes with spatial sections being a product of two maximally symmetric spaces. If neither of the spaces has negative curvature, no Lorentzian solutions exist. If one of the subspaces is flat, and the other has negative curvature, the Lorentzian Hartle-Hawking ground state is the Minkowski space with a specific parametrization chosen by the boundary term in the action. We analyze the propagation of wave packets in the minisuperspace of the model with both subspaces of negative curvature. Both the wave packets and classical trajectories oscillate if the number of space-time dimensions is less than ten. However, the wave packets do not follow classical trajectories, although they are (in principle) distinguishable even after a large number of oscillations, in contrast with the gravity-scalar-field model. © 1990 The American Physical Society.