Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Cosmological Relational Model of Shape and Scale in 1-d   Relational particle models are useful toy models for quantum cosmology and
the problem of time in quantum general relativity. This paper shows how to
extend existing work on concrete examples of relational particle models in 1-d
to include a notion of scale. This is useful as regards forming a tight analogy
with quantum cosmology and the emergent semiclassical time and hidden time
approaches to the problem of time. This paper shows furthermore that the
correspondence between relational particle models and classical and quantum
cosmology can be strengthened using judicious choices of the mechanical
potential. This gives relational particle mechanics models with analogues of
spatial curvature, cosmological constant, dust and radiation terms. A number of
these models are then tractable at the quantum level. These models can be used
to study important issues 1) in canonical quantum gravity: the problem of time,
the semiclassical approach to it and timeless approaches to it (such as the
naive Schrodinger interpretation and records theory). 2) In quantum cosmology,
such as in the investigation of uniform states, robustness, and the qualitative
understanding of the origin of structure formation.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex