Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex and real Hermite polynomials and related quantizations   It is known that the anti-Wick (or standard coherent state) quantization of
the complex plane produces both canonical commutation rule and quantum spectrum
of the harmonic oscillator (up to the addition of a constant). In the present
work, we show that these two issues are not necessarily coupled: there exists a
family of separable Hilbert spaces, including the usual Fock-Bargmann space,
and in each element in this family there exists an overcomplete set of
unit-norm states resolving the unity. With the exception of the Fock-Bargmann
case, they all produce non-canonical commutation relation whereas the quantum
spectrum of the harmonic oscillator remains the same up to the addition of a
constant. The statistical aspects of these non-equivalent coherent states
quantizations are investigated. We also explore the localization aspects in the
real line yielded by similar quantizations based on real Hermite polynomials.

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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol