Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Background Field Approximation in (quantum) cosmology   We analyze the Hamilton-Jacobi action of gravity and matter in the limit
where gravity is treated at the background field approximation. The motivation
is to clarify when and how the solutions of the Wheeler-DeWitt equation lead to
the Schr\"odinger equation in a given background. To this end, we determine
when and how the total action, solution of the constraint equations of General
Relativity, leads to the HJ action for matter in a given background. This is
achieved by comparing two neighboring solutions differing slightly in their
matter energy content. To first order in the change of the 3-geometries, the
change of the gravitational action equals the integral of the matter energy
evaluated in the background geometry. Higher order terms are governed by the
``susceptibility'' of the geometry. These classical properties also apply to
quantum cosmology since the conditions which legitimize the use of WKB
gravitational waves are concomitant with those governing the validity of the
background field approximation.

14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
2
The categories of this paper are: math