Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable structures and the quantization of free null initial data for
  gravity   Variables for constraint free null canonical vacuum general relativity are
presented which have simple Poisson brackets that facilitate quantization. Free
initial data for vacuum general relativity on a pair of intersecting null
hypersurfaces has been known since the 1960s. These consist of the "main" data
which are set on the bulk of the two null hypersurfaces, and additional
"surface" data set only on their intersection 2-surface. More recently the
complete set of Poisson brackets of such data has been obtained. However the
complexity of these brackets is an obstacle to their quantization. Part of this
difficulty may be overcome using methods from the treatment of cylindrically
symmetric gravity. Specializing from general to cylindrically symmetric
solutions changes the Poisson algebra of the null initial data surprisingly
little, but cylindrically symmetric vacuum general relativity is an integrable
system, making powerful tools available. Here a transformation is constructed
at the cylindrically symmetric level which maps the main initial data to new
data forming a Poisson algebra for which an exact deformation quantization is
known. (Although an auxiliary condition on the data has been quantized only in
the asymptotically flat case, and a suitable representation of the algebra of
quantum data by operators on a Hilbert space has not yet been found.) The
definition of the new main data generalizes naturally to arbitrary,
symmetryless gravitational fields, with the Poisson brackets retaining their
simplicity. The corresponding generalization of the quantization is however
ambiguous and requires further analysis.

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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: stat
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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: physics
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The categories of this paper are: nlin
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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: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg