Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebras with convergent star products and their representations in
  Hilbert spaces   We study star product algebras of analytic functions for which the power
series defining the products converge absolutely. Such algebras arise naturally
in deformation quantization theory and in noncommutative quantum field theory.
We consider different star products in a unifying way and present results on
the structure and basic properties of these algebras, which are useful for
applications. Special attention is given to the Hilbert space representation of
the algebras and to the exact description of their corresponding operator
algebras.

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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con