Half-Sided modular inclusions of von-Neumann-Algebras

Wiesbrock, Hans‐Werner

doi:10.1007/bf02098019

Cited by 102 publications

(129 citation statements)

References 11 publications

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“…It is a striking fact that one can reconstruct from a few algebras in this specific position a unitary representation of the space-time symmetry group, the PCT operator and the net of local algebras [19,20]. This observation substantiates the claim that the dynamical information of a theory is contained in the relative position of the underlying algebras.…”

Section: Local Algebras and Their Inclusionssupporting

confidence: 66%

Current Trends in Axiomatic Quantum Field Theory

Buchholz

2000

Quantum Field Theory

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In this article a non-technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras of observables, their relation to the underlying fields and the significance of their relative positions. Moreover, the physical interpretation of the theory is discussed with emphasis on problems appearing in gauge theories, such as the revision of the particle concept, the determination of symmetries and statistics from the superselection structure, the analysis of the short distance properties and the specific features of relativistic thermal states. Some problems appearing in quantum field theory on curved spacetimes are also briefly mentioned.

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Section: Local Algebras and Their Inclusionssupporting

confidence: 66%

Current Trends in Axiomatic Quantum Field Theory

Buchholz

2000

Quantum Field Theory

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“…The modular theory was significantly enriched by the concept of modular inclusion and of modular intersection [42] [43]. These structures are related to a generalization of the Takesaki theorem in section 2: instead of requiring that the modular group of the larger algebra acts as a one-parametric automorphism group on the smaller, one only assumes that it contracts the algebra in one direction (± halfsided modular inclusions).…”

Section: A Some Facts About Modular Operator Theorymentioning

confidence: 99%

Addendum to ‘Area density of localization entropy: I. The case of wedge localization’

Schroer¹

2007

Class. Quantum Grav.

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Using an appropriately formulated holographic lightfront projection, we derive an area law for the localization-entropy caused by vacuum polarization on the horizon of a wedge region. Its area density has a simple kinematic relation to the volume extensive heat bath entropy of the lightfront algebra. Apart from a change of parametrization, the infinite lightlike length contribution to the lightfront volume factor corresponds to the short-distance divergence of the area density of the localization entropy. This correspondence is a consequence of the conformal invariance of the lightfront holography combined with the well-known fact that conformality relates short to long distances. In the explicit calculation of the strength factor we use the temperature duality relation of rational chiral theories whose derivation will be briefly reviewed. We comment on the potential relevance for the understanding of Black hole entropy.

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“…By the geodesic KMS property, we get that A(µ 1 (W )) ⊂ A(W ) is a half-sided modular inclusion. Therefore the theorem of Wiesbrock [55] gives a one-parameter group V with positive generator such that V (1)A(W )V (−1) = A(µ 1 (W )) and satisfying the Borchers commutation relations…”

Section: Dethermalization With Noncommutative Flowsmentioning

confidence: 99%

“…Remark 4.11. The unitary group V is constructed by the Borchers-Wiesbrock methods [4,5,55] and, in the conformal case, coincides with the previously considered one where the geometric meaning is complete.…”

Section: Introductionmentioning

confidence: 99%

A Converse Hawking-Unruh Effect and dS2/CFT Correspondence

Guido

Longo

2003

Ann. Henri Poincaré

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Given a local quantum field theory net A on the de Sitter spacetime dS d , where geodesic observers are thermalized at Gibbons-Hawking temperature, we look for observers that feel to be in a ground state, i.e., particle evolutions with positive generator, providing a sort of converse to the Hawking-Unruh effect. Such positive energy evolutions always exist as noncommutative flows, but have only a partial geometric meaning, yet they map localized observables into localized observables.We characterize the local conformal nets on dS d . Only in this case our positive energy evolutions have a complete geometrical meaning. We show that each net has a unique maximal expected conformal subnet, where our evolutions are thus geometrical.In the two-dimensional case, we construct a holographic one-to-one correspondence between local nets A on dS 2 and local conformal non-isotonic families (pseudonets) B on S 1 . The pseudonet B gives rise to two local conformal nets B ± on S 1 , that correspond to the H ± horizon components of A, and to the chiral components of the maximal conformal subnet of A. In particular, A is holographically reconstructed by a single horizon component, namely the pseudonet is a net, iff the translations on H ± have positive energy and the translations on H ∓ are trivial. This is the case iff the one-parameter unitary group implementing rotations on dS 2 has positive/negative generator.

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Half-Sided modular inclusions of von-Neumann-Algebras

Cited by 102 publications

References 11 publications

Current Trends in Axiomatic Quantum Field Theory

Current Trends in Axiomatic Quantum Field Theory

Addendum to ‘Area density of localization entropy: I. The case of wedge localization’

A Converse Hawking-Unruh Effect and dS2/CFT Correspondence

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