Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-Adjoint Wheeler-DeWitt Operators, the Problem of Time and the Wave
  Function of the Universe   We discuss minisuperspace aspects a non empty Robertson-Walker universe
containing scalar matter field. The requirement that the Wheeler-DeWitt (WDW)
operator be self adjoint is a key ingredient in constructing the physical
Hilbert space and has non-trivial cosmological implications since it is related
with the problem of time in quantum cosmology. Namely, if time is parametrized
by matter fields we find two types of domains for the self adjoint WDW
operator: a non trivial domain is comprised of zero current (Hartle-Hawking
type) wave functions and is parametrized by two new parameters, whereas the
domain of a self adjoint WDW operator acting on tunneling (Vilenkin type) wave
functions is a {\em single} ray. On the other hand, if time is parametrized by
the scale factor both types of wave functions give rise to non trivial domains
for the self adjoint WDW operators, and no new parameters appear in them.

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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: ao-sci