Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of Self-Adjoint Berezin-Toeplitz Operators on Kahler
  Manifolds and a Probabilistic Representation of the Associated Semigroups   We investigate a class of operators resulting from a quantization scheme
attributed to Berezin. These so-called Berezin-Toeplitz operators are defined
on a Hilbert space of square-integrable holomorphic sections in a line bundle
over the classical phase space. As a first goal we develop self-adjointness
criteria for Berezin-Toeplitz operators defined via quadratic forms. Then,
following a concept of Daubechies and Klauder, the semigroups generated by
these operators may under certain conditions be represented in the form of
Wiener-regularized path integrals. More explicitly, the integration is taken
over Brownian-motion paths in phase space in the ultra-diffusive limit. All
results are the consequence of a relation between Berezin-Toeplitz operators
and Schrodinger operators defined via certain quadratic forms. The
probabilistic representation is derived in conjunction with a version of the
Feynman-Kac formula.

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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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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-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol