Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nets of Subfactors   A subtheory of a quantum field theory specifies von~Neumann subalgebras
$\aa(\oo)$ (the `observables' in the space-time region $\oo$) of the
von~Neumann algebras $\bb(\oo)$ (the `fields' localized in $\oo$). Every local
algebra being a (type $\III_1$) factor, the inclusion $\aa(\oo) \subset
\bb(\oo)$ is a subfactor. The assignment of these local subfactors to the
space-time regions is called a `net of subfactors'. The theory of subfactors is
applied to such nets. In order to characterize the `relative position' of the
subtheory, and in particular to control the restriction and induction of
superselection sectors, the canonical endomorphism is studied. The crucial
observation is this: the canonical endomorphism of a local subfactor extends to
an endomorphism of the field net, which in turn restricts to a localized
endomorphism of the observable net. The method allows to characterize, and
reconstruct, local extensions $\bb$ of a given theory $\aa$ in terms of the
observables. Various non-trivial examples are given.

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics