Classification of subsystems for graded-local nets with trivial superselection structure

Classification of Subsystems for Local Nets with Trivial Superselection Structure

Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is the fixed point net under a compact group action on one component in a suitable tensor product decomposition of F. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors.

Superselection Theory for Subsystems

An inclusion of observable nets satisfying duality induces an inclusion of canonical field nets. Any Bose net intermediate between the observable net and the field net and satisfying duality is the fixed-point net of the field net under a compact group. This compact group is its canonical gauge group if the occurrence of sectors with infinite statistics can be ruled out for the observable net and its vacuum Hilbert space is separable.

Massless scalar free Field in 1+1 dimensions, II: Net Cohomology and Completeness of Superselection Sectors

As an application of Roberts' cohomology (net cohomology), we prove the completeness of the DHR sectors of the local observables of the model in the title, detailed in [8]. This result is achieved via the triviality of the net 1-cohomology, with values in the local fields, enhancing the Roberts' methods to the case of anyonic Weyl nets, not satisfying the split property. We take advantage of using different causal index sets for the nets involved. The presence of anyonic commutation relations is treated introducing the notion of nets graded by a generic group, and the related properties of gra…

Representations of nets of C*-algebras over S^1

In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account of the effects of the fundamental group of the spacetime. Using this notion of representation, we prove that any net of C*-algebras over S^1 admits faithful representations, and when the net is covariant under Diff(S^1), it admits representations covariant under any amenable subgroup of Diff(S^1).

von Neumann 代数偏序集的超选 sectors

Superselection sectors for posets of von Neumann algebras

本文为带反序对合的 von Neumann 代数偏序集建立几何公理，构造超选 sectors 的辫张量范畴，并证明其与二维量子自旋系统相关范畴等价。

Asymptotic morphisms and superselection theory in the scaling limit

Given a local Haag-Kastler net of von Neumann algebras and one of its scaling limit states, we introduce a variant of the notion of asymptotic morphism by Connes and Higson, and we show that the unitary equivalence classes of (localized) morphisms of the scaling limit theory of the original net are in bijection with classes of suitable pairs of such asymptotic morphisms. In the process, we also show that the quasi-local C*-algebras of two nets are isomorphic under very general hypotheses, and we construct an extension of the scaling algebra whose representation on the scaling limit Hilbert spa…