Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Supmech: the Geometro-statistical Formalism Underlying Quantum Mechanics   As the first step in an approach to the solution of Hilbert's sixth problem,
a general scheme of mechanics, called `supmech', is developed integrating
noncommutative symplectic geometry and noncommutative probability theory in an
algebraic framework; it has quantum mechanics (QM) and classical mechanics as
special subdisciplines and facilitates an autonomous development of QM and
satisfactory treatments of quantum-classical correspondence and quantum
measurements (including a straightforward \emph{derivation} of the von Neumann
reduction rule). The scheme associates, with every `experimentally accessible'
system, a symplectic superalgebra and operates essentially as noncommutative
Hamiltonian mechanics incorporating the extra condition that the sets of
observables and pure states be mutually separating. The latter condition serves
to smoothly connect the algebraically defined quantum systems to ilbert
space-based ones; the rigged Hilbert space - based Dirac bra-ket formalism
naturally appears. The formalism has a natural place for commutative
superselection rules. Noncommutative analogues of objects like the momentum map
and the Poincar$\acute{e}$-Cartan form are introduced and some related
symplectic geometry developed.

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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int