July 2, 2010
A review of the Hodge and Hopf-algebraic approach to QFT.
January 30, 2012
Recent progress about "modular localization" reveals that, as a result of the S-Matrix in its role of a "relative modular invariant of wedge-localization, one obtains a new non-perturbative constructive setting of local quantum physicis which only uses intrinsic (independent of quantization) properties. The main point is a derivation of the particle crossing property from the KMS identity of wedge-localized subalgebras in which the connection of incoming/outgoing particles wi...
February 25, 2014
Integrable quantum field theories in 1+1 dimensions have recently become amenable to a rigorous construction, but many questions about the structure of their local observables remain open. Our goal is to characterize these local observables in terms of their expansion coefficients in a series expansion by interacting annihilators and creators, similar to form factors. We establish a rigorous one-to-one characterization, where locality of an observable is reflected in analytic...
October 30, 1997
The recently proposed constructive approach to nonperturbative QFT, based on modular localization, is reviewed and extended. It allows to unify black holes physics and H-temperatures (H standing for Hawking or Horizon) with the bootstrap-formfactor program for nonperturbative construction of low dimensional QFT. In case of on-shell particle number conservation, the equations characterizing the modular localization spaces for wedges are Bethe-Ansatz equation in the form as rec...
February 21, 2005
Starting from a given factorizing S-matrix $S$ in two space-time dimensions, we review a novel strategy to rigorously construct quantum field theories describing particles whose interaction is governed by $S$. The construction procedure is divided into two main steps: Firstly certain semi-local Wightman fields are introduced by means of Zamolodchikov's algebra. The second step consists in proving the existence of local observables in these models. As a new result, an intermed...
November 27, 2000
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but has also proven to be useful in the rigorous treatment of models. In this contribution a non-technical survey is given with emphasis on interesting recent developments and future perspectives. Topics covered are the relation between the algeb...
November 21, 2001
The previously developed algebraic lightfront holography is used in conjunction with the tensor splitting of the chiral theory on the causal horizon. In this way a universal area law for the entanglement entropy of the vacuum relative to the split (tensor factorized) vacuum is obtained. The universality of the area law is a result of the kinematical structure of the properly defined lightfront degrees of freedom. We consider this entropy associated with causal horizon of the ...
July 5, 2005
Using an appropriatly 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 lighlike length contribution to the lightfront volume factor corresponds to the short-distance divergence of the area density o...
June 11, 2009
It is often overlooked that local quantum physics has a built in quantum localization structure which may under certain circumstances disagree with (differential, algebraic) geometric ideas. String theory originated from such a spectacular misinterpretation of a source-target embedding in which an inner symmetry of the source object becomes the Lorentz symmetry of the target space. The quantum localization reveals however that the resulting object is an infinite component poi...
April 11, 2011
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an infinite class of explicit examples is constructed on the Borchers-Uhlmann algebra underlying Wightman quantum field theory. These deformations exist independently of the space-time dimension, and contain the recently studied warped convolut...