  The Hawking minisuperspace model (closed FRW geometry with a homogeneous
massive scalar field) provides a fairly non-trivial testing ground for
fundamental problems in quantum cosmology. We provide evidence that the
Wheeler-DeWitt equation admits a basis of solutions that is distinguished by
analyticity properities in a large scale factor expansion. As a consequence,
the space of solutions decomposes in a preferred way into two Hilbert spaces
with positive and negative definite scalar product, respectively. These results
may be viewed as a hint for a deeper significance of analyticity. If a similar
structure exists in full (non-minisuperspace) models as well, severe
implications on the foundations of quantum cosmology are to be expected.
Semiclassically, the elements of the preferred basis describe contracting and
expanding universes with a prescribed value of the matter (scalar field)
energy. Half of the basis elements have previously been constructed by Hawking
and Page in a wormhole context, and they appear in a new light here. The
technical tools to arrive at these conclusions are transformations of the wave
function into several alternative representations that are based on the
harmonic oscillator form of the matter energy operator, and that are called
oscillator, energy and Fock representation. The framework defined by these may
be of some help in analyzing the Wheeler-DeWitt equation for other purposes as
well.
