Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Gravity on a Circle and the Diffeomorphism Invariance of the
  Schrodinger Equation   We study a model for quantum gravity on a circle in which the notion of a
classical metric tensor is replaced by a quantum metric with an inhomogeneous
transformation law under diffeomorphisms. This transformation law corresponds
to the co--adjoint action of the Virasoro algebra, and resembles that of the
connection in Yang--Mills theory. The transformation property is motivated by
the diffeomorphism invariance of the one dimensional Schr\"odinger equation.
The quantum distance measured by the metric corresponds to the phase of a
quantum mechanical wavefunction. The dynamics of the quantum gravity theory are
specified by postulating a Riemann metric on the space $Q$ of quantum metrics
and taking the kinetic energy operator to be the resulting laplacian on the
configuration space $Q/\rm Diff_0(S^1)$. The resulting metric on the
configuration space is analyzed and found to have singularities. The
second--quantized Schr\"odinger equation is derived, some exact solutions are
found, and a generic wavefunction behavior near one of the metric singularities
is described. Finally some further directions are indicated, including an
analogue of the Yamabe problem of differential geometry.

8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
18
The categories of this paper are: econ