Local normality in Quantum Statistical Mechanics

Takesaki, Masamichi; Winnink, M.

doi:10.1007/bf01645976

Cited by 42 publications

(36 citation statements)

References 26 publications

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“…Takesaki and Winnink [44] have shown that a locally normal state decomposes into locally normal states, if the split property holds. We shall show here analogous results for localizable representations (sectors).…”

Section: Disintegration Of Locally Normal Representations and Of Sementioning

confidence: 99%

Multi-Interval Subfactors and Modularity¶of Representations in Conformal Field Theory

Kawahigashi¹,

Longo²,

Müger³

2001

Commun. Math. Phys.

208

536

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We describe the structure of the inclusions of factors A(E) ⊂ A(E ) associated with multi-intervals E ⊂ R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. In particular, if the net is conformal and the subfactor has finite index, the inclusion associated with two separated intervals is isomorphic to the Longo-Rehren inclusion, which provides a quantum double construction of the tensor category of superselection sectors of A. As a consequence, the index of A(E) ⊂ A(E ) coincides with the global index associated with all irreducible sectors, the braiding symmetry associated with all sectors is non-degenerate, namely the representations of A form a modular tensor category, and every sector is a direct sum of sectors with finite dimension. The superselection structure is generated by local data. The same results hold true if conformal invariance is replaced by strong additivity and there exists a modular PCT symmetry.

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Section: Disintegration Of Locally Normal Representations and Of Sementioning

confidence: 99%

Multi-Interval Subfactors and Modularity¶of Representations in Conformal Field Theory

Kawahigashi¹,

Longo²,

Müger³

2001

Commun. Math. Phys.

208

536

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“…By the argument in the appendix of [14], the fact that ω ξ A 0,ι (O ) = ω 0,ι A 0,ι (O ), together with translation covariance of π ξ , imply (8.4) if it is known that property B holds in the representation π ξ . But if H vac 0,ι is separable, then each local algebra π vac 0,ι (A 0,ι (O)) has a separable predual, and being ω ξ locally normal, from [36,Corollary 3.2] it follows that the Hilbert space H ξ of π ξ is separable, and then, by the already recalled argument of Roberts [32], property B holds in the representation π ξ .…”

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confidence: 99%

Scaling Algebras for Charged Fields and Short-Distance Analysis for Localizable and Topological Charges

D’Antoni

Morsella

Verch

2004

Ann. Henri Poincaré

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The method of scaling algebras, which has been introduced earlier as a means for analyzing the short-distance behavior of quantum field theories in the setting of the model-independent, operator algebraic approach, is extended to the case of fields carrying superselection charges. In doing so, consideration will be given to strictly localizable charges ("DHR-type" superselection charges) as well as to charges which can only be localized in regions extending to spacelike infinity ("BF-type" superselection charges). A criterion for the preservance of superselection charges in the short-distance scaling limit is proposed. Consequences of this preservance of superselection charges are studied. The conjugate charge of a preserved charge is also preserved, and for charges of DHR-type, the preservance of all charges of a quantum field theory in the scaling limit leads to equivalence of local and global intertwiners between superselection sectors.

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“…This set K( * ∞ 1 A, * ∞ 1 σ) is a compact affine set in the weak * -topology and is known to be a Choquet simplex whose extreme points are those φ ∈ K( * ∞ 1 A, * ∞ 1 σ), the von Neumann algebras generated by images of whose GNS-representations are factors (cf. [5], [9] and [11]).…”

Section: The Simplex Of Kms Quantum Symmetric Statesmentioning

confidence: 99%

KMS quantum symmetric states

Dykema

Mukherjee

2017

Journal of Mathematical Physics

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Let $A$ be a unital C$^*$-algebra and let $\sigma$ be a one-parameter automorphism group of $A$. We consider $\operatorname{QSS}_\sigma(A)$, the set of all quantum symmetric states on $*_1^\infty A$ that are also KMS states (for a fixed inverse temperature, for specificity taken to be $-1$) for the free product automorphism group $*_1^\infty\sigma$. We characterize the elements of $\operatorname{QSS}_\sigma(A)$, we show that $\operatorname{QSS}_\sigma(A)$ is a Choquet simplex whenever it is nonempty and we characterize its extreme points.Comment: 14 page

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Local normality in Quantum Statistical Mechanics

Cited by 42 publications

References 26 publications

Multi-Interval Subfactors and Modularity¶of Representations in Conformal Field Theory

Multi-Interval Subfactors and Modularity¶of Representations in Conformal Field Theory

Scaling Algebras for Charged Fields and Short-Distance Analysis for Localizable and Topological Charges

KMS quantum symmetric states

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