Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry Reduction of States I   We develop a general theory of symmetry reduction of states on (possibly
non-commutative) *-algebras that are equipped with a Poisson bracket and a
Hamiltonian action of a commutative Lie algebra $g$. The key idea advocated for
in this article is that the "correct" notion of positivity on a *-algebra $A$
is not necessarily the algebraic one whose positive elements are the sums of
Hermitian squares $a^* a$ with $a \in A$, but can be a more general one that
depends on the example at hand, like pointwise positivity on *-algebras of
functions or positivity in a representation as operators. The notion of states
(normalized positive Hermitian linear functionals) on $A$ thus depends on this
choice of positivity on $A$, and the notion of positivity on the reduced
algebra $A_{red}$ should be such that states on $A_{red}$ are obtained as
reductions of certain states on $A$. In the special case of the *-algebra of
smooth functions on a Poisson manifold $M$, this reduction scheme reproduces
the coisotropic reduction of $M$, where the reduced manifold $M_{red}$ is just
a geometric manifestation of the reduction of the evaluation functionals
associated to certain points of $M$. However, we are mainly interested in
applications to non-formal deformation quantization and therefore also discuss
the reduction of the Weyl algebra, and of the polynomial algebra whose
non-commutative analogs we plan to examine in future projects.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph