Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hagedorn--Hermite Correspondence   We investigate the relationship between the semiclassical wave packets of
Hagedorn and the Hermite functions by establishing a relationship between their
ladder operators. This Hagedorn--Hermite correspondence provides a unified view
as well as simple proofs of some essential results on the Hagedorn wave
packets. Particularly, we show that Hagedorn's ladder operators are a natural
set of ladder operators obtained from the position and momentum operators using
the symplectic group. This construction reveals an algebraic structure of the
Hagedorn wave packets, and explains the relative simplicity of Hagedorn's
parametrization compared to the rather intricate construction of the
generalized squeezed states. We apply our formulation to show the existence of
minimal uncertainty products for the Hagedorn wave packets, generalizing
Hagedorn's one-dimensional result to multi-dimensions. The Hagedorn--Hermite
correspondence also leads to an alternative derivation of the generating
function for the Hagedorn wave packets based on the generating function for the
Hermite functions. This result, in turn, reveals the relationship between the
Hagedorn polynomials and the Hermite polynomials.

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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th