Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional Integral Approach to $C^*$-algebraic Quantum Mechanics II:
  Symplectic Quantum Mechanics   We propose $Sp\,(8,\R)$ and its Langlands dual $SO(9,\R)$ as dynamical groups
for closed quantum systems. Restricting here to the non-compact group
$Sp\,(8,\R)$, the quantum theory is constructed and investigated. The
functional Mellin transform plays a prominent role in defining the quantum
theory. It provides a bridge between the quantum algebra of observables and the
algebra of operators on Hilbert spaces furnishing unitary representations that
are induced from a distinguished parabolic subgroup of $Sp\,(8,\C)$. As well,
the parabolic subgroup renders a fiber bundle construction that models what can
be described as a matrix quantum gauge theory. The formulation is strictly
quantum mechanics: no \emph{a priori} space-time is assumed and the only
geometrical input comes indirectly from the group manifold. But what appears on
the surface to be a fairly simple-minded model turns out to have a capacious
structure suggesting some compelling physical interpretations regarding
space-time and fundamental interactions.

28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio