相关论文: Type of local von Neumann algebras in abelian quan…

We will argue in this paper that the type classification of v.Neumann algebras play an important role in a theory of quantum gravity and quantum space-time physics. We provide arguments that type $II_{\infty}$ and its representation as a…

We prove that for any two commuting von Neumann algebras of infinite type, the open set of Bell correlated states for the two algebras is norm dense. We then apply this result to algebraic quantum field theory -- where all local algebras…

Consider a compact locally symmetric space $M$ of rank $r$, with fundamental group $\Gamma$. The von Neumann algebra $\vn(\Gamma)$ is the convolution algebra of functions $f\in\ell_2(\Gamma)$ which act by left convolution on…

In the present paper we prove that every 2-local derivation on a von Neumann algebra of type I is a derivation.

We show that the KMS_beta-states of Bost-Connes type systems for number fields in the region 0<beta\le 1, as well as of the Connes-Marcolli GL_2-system for 1<beta\le 2, have type III_1. This is equivalent to ergodicity of various actions on…

We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we…

It is shown that under the assumption of the nuclearity condition for local regions the resulting Doplicher-Longo-algebra between two double cones which due to nuclearity is type I allows to estimate its entropy by nuclearity bounds.

This paper focuses on the generalized version of the quantum double model on arbitrary $N$-dimensional simplicial complexes with finite local regularity. The core of our analysis is a detailed characterization of the frustration-free ground…

We construct a Type II$_\infty$ von Neumann algebra that describes the large $N$ physics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative $1/N$ corrections. Using only the…

We show that every ring isomorphism between the algebras of locally measurable operators for type II$_\infty$ von Neumann algebras is similar to a real $^*$-isomorphism. This together with previous results by the author and…

We prove Haag duality for conelike regions in the ground state representation corresponding to the translational invariant ground state of Kitaev's quantum double model for finite abelian groups. This property says that if an observable…

We find new type II backgrounds with non-relativistic symmetries via non-Abelian T-duality. First we consider geometries with Galilean symmetries in type IIA, which have been identified as non-relativistic generalizations of the ABJM…

It is proposed that a non-Abelian adjoint two-form in BF type theories transform inhomogeneously under the gauge group. The resulting restrictions on invariant actions are discussed. The auxiliary one-form which is required for maintaining…

The von Neumann algebra free product of arbitary finite dimensional von Neumann algebras with respect to arbitrary faithful states, at least one of which is not a trace, is found to be a type~III factor possibly direct sum a finite…

We describe an algebra of observables for a static patch in de Sitter space, with operators gravitationally dressed to the worldline of an observer. The algebra is a von Neumann algebra of Type II$_1$. There is a natural notion of entropy…

For nonlinear models of an Abelian vector supermultiplet coupled to N = 2 supergravity in four dimensions, we formulate the self-duality equation which expresses invariance under U(1) duality rotations. In the flat space limit, this…

Using methods coming from non-formal equivariant quantization, we construct in this short note a unitary dual 2-cocycle on a discrete family of quotient groups of subgroups of the affine group of a local field (which is not of…

In this paper we are interested in examples of locally compact quantum groups $(M,\Delta)$ such that both von Neumann algebras, $M$ and the dual $\hat{M}$, are factors. There is a lot of known examples such that $(M,\hat{M})$ are…

An intriguing feature of type II$_1$ von Neumann algebra is that the entropy of the mixed states is negative. Although the type classification of von Neumann algebra and its consequence in holography have been extensively explored recently,…

The present paper presents a survey of some recent results devoted to derivations, local derivations and 2-local derivations on various algebras of measurable operators affiliated with von Neumann algebras. We give a complete description of…