Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relational Quadrilateralland Interpretation of CP^2 and Quotients   I investigate qualitatively significant regions of the configuration space
for the classical and quantum mechanics of the relational quadrilateral in 2-d.
This is relational in the sense that only relative ratios of separations,
relative angles and relative times are significant. Such relational particle
mechanics models have many analogies with the geometrodynamical formulation of
general relativity. Thus, they are suitable as toy models for studying 1)
problem of time in quantum gravity strategies, in particular timeless,
semiclassical and histories theory approaches and combinations of these. 2)
Various other quantum-cosmological issues, such as structure
formation/inhomogeneity and the significance of uniform states. The relational
quadrilateral is more useful in these respects than previously investigated
simpler RPM's as it possesses linear constraints, nontrivial subsystems and its
configuration space is a nontrivial complex-projective space. In this paper, I
investigate the submanifold of collinear configurations, the submanifolds with
a single-particle collision, the square configurations and regions of the
configuration space for which such as approximate collinearity, approximate
squareness and approximate triangularity hold. I consider both mirror image
identified and unidentified shapes, as well as both distinguishable and
indistinguishable particle labels. I find the following CP^2 coordinate systems
to be useful to these ends. 1) Kuiper's coordinates, which, for
quadrilateralland, are magnitudes of the Jacobi vectors and anisoscelesnesses
of the triangles formed between them. 2) Gibbons-Pope type coordinates, which,
for quadrilateralland, are the sum and difference of relative angles between
subsystems, the ratio of size of 2 subsystems and the proportion of universe
model occupied by the subsystems.

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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg