A Comment on Jones Inclusions with infinite Index

Given an irreducible inclusion of infinite von-Neumann-algebras \cn \subset \cm together with a conditional expectation E : \cm \rightarrow \cm such that the inclusion has depth 2, we show quite explicitely how \cn can be viewed as the fixed point algebra of \cm w.r.t. an outer action of a compact Kac-algebra acting on \cm. This gives an alternative proof, under this special setting of a more general result of M. Enock and R. Nest, [E-N], see also S. Yamagami, [Ya2].Comment: latex, 40 page

Looking beyond the Thermal Horizon: Hidden Symmetries in Chiral 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 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 sytem 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.Comment: 17 pages, tcilatex, still more typos removed and one reference correcte

Weak Hopf Algebras and Reducible Jones Inclusions of Depth 2. I: From Crossed products to Jones towers

We apply the theory of finite dimensional weak C^*-Hopf algebras A as developed by G. B\"ohm, F. Nill and K. Szlach\'anyi to study reducible inclusion triples of von-Neumann algebras N \subset M \subset (M\cros\A). Here M is an A-module algebra, N is the fixed point algebra and \M\cros\A is the crossed product extension. ``Weak'' means that the coproduct \Delta on A is non-unital, requiring various modifications of the standard definitions for (co-)actions and crossed products. We show that acting with normalized positive and nondegenerate left integrals l\in\A gives rise to faithful conditional expectations E_l: M-->N, where under certain regularity conditions this correspondence is one-to-one. Associated with such left integrals we construct ``Jones projections'' e_l\in\A obeying the Jones relations as an identity in M\cros\A. Finally, we prove that N\subset M always has finite index and depth 2 and that the basic Jones construction is given by the ideal M_1:=M e_l M \subset M\cros\A, where under appropriate conditions M_1 = M\cros\A. In a subsequent paper we will show that converseley any reducible finite index and depth-2 Jones tower of von-Neumann factors (with finite dimensional centers) arises in this way.Comment: Latex, 63 page

Modular Groups of Quantum Fields in Thermal States

For a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under half-sided translations. The modular flows associated with the algebras of the forward light cone and a space-like wedge admit a simple geometric description in two dimensional models that factorize in light-cone coordinates. At large distances from the domain boundary compared to the inverse temperature the flow pattern is essentially the same as time translations, whereas the zero temperature results are approximately reproduced close to the edge of the wedge and the apex of the cone. Associated with each domain there is also a one parameter group with a positive generator, for which the thermal state is a ground state. Formally, this may be regarded as a certain converse of the Unruh-effect.Comment: 28 pages, 4 figure

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

Comment on: Modular Theory and Geometry

In this note we comment on part of a recent article by B. Schroer and H.-W. Wiesbrock. Therein they calculate some new modular structure for the U(1)-current-algebra (Weyl-algebra). We point out that their findings are true in a more general setting. The split-property allows an extension to doubly-localized algebras.Comment: 13 pages, corrected versio

Poly(hydroxy alkanoate)s in Medical Applications

This review summarizes the state-of-the-art knowledge of the usage of poly(hydroxy alkanoate)s in medical and sanitary applications. Depending on the monomers incorporated into the polymers and copolymers, this class of polymers exhibits a broad range of (thermo-)plastic properties, enabling their processing by, e.g., solution casting or melt extrusion. In this review, strategies for the polymer analogous modification of these materials and their surfaces are highlighted and correlated with the potential applications of the corresponding materials and blends. While the commercial availability of purified PHAs is addressed in brief, special focus is put on the (bio-)degradability of these polymers and ways to influence the degradation mechanism and/or the duration of degradation

UV-Induced Crosslinking of Poly[2-(2’-Norbornenyl)-2-Oxazoline]s

A 2-oxazoline monomer bearing a norbornenyl functionality in the side-chain was prepared from the reaction of 5-norbornene-2-carbonitrile and 2-ethanol amine. This monomer could be successfully polymerized using a 2-oxazolinium-based macroinitiator that was in-situ generated from the methyl cation-initiated oligomerization of 2-ethyl-2-oxazoline. This polymer could be subjected to polymeranalogous reactions involving the alkene groups of the norbornenyl side-chains: A proof-of-concept was established by utilizing the polymers in photoresists that were crosslinked by thiol-ene reactions involving bisfunctional thiols. Photoinitiators for the UV-induced thiol-ene reaction were required in catalytic amounts only. After development, the resists exhibited reproduction of the geometric patterns with a resolution of 30 μm