An algebraic Haag's theorem

Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with bases on a fixed space-like hyperplane completely determines an algebraic QFT model. More precisely, if for two models there is unitary connecting all of these algebras, then --- without assuming that this unitary also connects their respective vacuum states or spacetime symmetry representations --- it follows that the two models are equivalent. This result might be viewed as an algebraic version of the celebrated theorem of Rudolf Haag about problems regarding the so-called "interaction-picture" in QFT. Original motivation of the author for finding such an algebraic version came from conformal chiral QFT. Both the chiral case as well as a related conjecture about standard half-sided modular inclusions will be also discussed

Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?

The question of what it means for a theory to describe the same physics on all spacetimes (SPASs) is discussed. As there may be many answers to this question, we isolate a necessary condition, the SPASs property, that should be satisfied by any reasonable notion of SPASs. This requires that if two theories conform to a common notion of SPASs, with one a subtheory of the other, and are isomorphic in some particular spacetime, then they should be isomorphic in all globally hyperbolic spacetimes (of given dimension). The SPASs property is formulated in a functorial setting broad enough to describe general physical theories describing processes in spacetime, subject to very minimal assumptions. By explicit constructions, the full class of locally covariant theories is shown not to satisfy the SPASs property, establishing that there is no notion of SPASs encompassing all such theories. It is also shown that all locally covariant theories obeying the time-slice property possess two local substructures, one kinematical (obtained directly from the functorial structure) and the other dynamical (obtained from a natural form of dynamics, termed relative Cauchy evolution). The covariance properties of relative Cauchy evolution and the kinematic and dynamical substructures are analyzed in detail. Calling local covariant theories dynamically local if their kinematical and dynamical local substructures coincide, it is shown that the class of dynamically local theories fulfills the SPASs property. As an application in quantum field theory, we give a model independent proof of the impossibility of making a covariant choice of preferred state in all spacetimes, for theories obeying dynamical locality together with typical assumptions.Comment: 60 pages, LaTeX. Version to appear in Annales Henri Poincar

Modular intersections of von-Neumann-algebras in quantum field theory

We show that modular intersections of von-Neumann-algebras occur naturally in 2+1-dim. quantum field theory. An example is given by the local observable algebras of wedge regions with a common lightray in the vacuum sector. Conversely, starting with a set of four algebras lying in a specified modular position relative to each other we construct a net of local observables of a 2+1 dim. quantum field theory. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(193) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Modular theory and geometry

In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is more on a programmatic side with many details remaining to be elaborated. (orig.)Available from TIB Hannover: RR 1596(352) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Symmetries and modular intersections of von-Neumann-algebras

SIGLEAvailable from TIB Hannover: RR 1596(192) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Looking beyond the thermal horizon: hidden symmetries in chrial models

In thermal states of chiral theories, as recently investigated by H.-J. Borchers and J. Yngvason, there exists a rich group of hidden symmetries. Here we show that this leads to a radical converse of the Hawking-Unruh observation in the following sense. The algebraic commutant of the algebra associated with a (heat bath) thermal chiral system can be used to reprocess the thermal system into a ground state system on a larger algebra with a larger localization space-time. This happens in such a way that the original system appears as a kind of generalized Unruh restriction of the ground state system and the thermal commutant as being transmutated into newly created 'virgin space-time region' behind a horizon. The related concepts of a 'chiral conformal core' and the possibility of a 'blow-up' of the latter suggest interesting ideas on localization of degrees of freedom with possible repercussion on how to define quantum entropy of localized matter content in Local Quantum Physics. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(364) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Modular constructions of quantum field theories with interactions

We extend the previously introduced constructive modular method to nonperturbative QFT. In particular the relevance of the concept of 'quantum localization' (via intersection of algebras) versus classical locality (via support properties of test functions) is explained in detail, the wedge algebras are constructed rigorously and the formal aspects of double cone algebras for d=1+1 factorizing theories are determined. The well-known on-shell crossing symmetry of the S-Matrix and of formfactors (cyclicity relation) in such theories is intimately related to the KMS properties of new quantum-local PFG (one-particle polarization-free) generators of these wedge algebras. These generators are 'on-shell'- and their Fourier transforms turn out to fulfill the Zamolodchikov-Faddeev algebra. As the wedge algebras contain the crossing symmetry informations, the double cone algebras reveal the particle content of fields. Modular theory associates with this double cone algebra two very useful chiral conformal quantum field theories which are the algebraic versions of the light ray algebras. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(365) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Extensions of conformal nets and superselection structures

Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Moebius group. We infer from this that every conformal net is normal and coronal, namely the local von Neumann algebra associated with an interval coincides with its double relative commutant inside the local von Neumann algebra associated with any larger interval. The net and the dual net give together rise to an infinite dimensional symmetry group, of which we study a class of positive energy irreducible representations. We mention how superselsection sectors extend to the dual net and we illustrate by examples how, in general, this process generates solitonic sectors. We describe the free theories associated with the lowest weight n representations of PSL(2, R), showing that they violate 3-regularity for n>2. When n#>=#2, we obtain examples of non Moebius-covariant sectors of a 3-regular (non 4-regular) net. (orig.)Available from TIB Hannover: RR 1596(255) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman