Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories

Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations of C*-dynamical systems with automorphic actions of R^n, whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita-Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations.Comment: 34 page

Deformations of Fermionic Quantum Field Theories and Integrable Models

Considering the model of a scalar massive Fermion, it is shown that by means of deformation techniques it is possible to obtain all integrable quantum field theoretic models on two-dimensional Minkowski space which have factorizing S-matrices corresponding to two-particle scattering functions S_2 satisfying S_2(0) = -1. Among these models there is for example the Sinh-Gordon model. Our analysis provides a complement to recent developments regarding deformations of quantum field theories. The deformed model is investigated also in higher dimensions. In particular, locality and covariance properties are analyzed.Comment: 20 page

On the equivalence of two deformation schemes in quantum field theory

Two recent deformation schemes for quantum field theories on the two-dimensional Minkowski space, making use of deformed field operators and Longo-Witten endomorphisms, respectively, are shown to be equivalent.Comment: 14 pages, no figure. The final version is available under Open Access. CC-B

String-- and Brane--Localized Causal Fields in a Strongly Nonlocal Model

We study a weakly local, but nonlocal model in spacetime dimension $d \geq 2$ and prove that it is maximally nonlocal in a certain specific quantitative sense. Nevertheless, depending on the number of dimensions $d$, it has string--localized or brane--localized operators which commute at spatial distances. In two spacetime dimensions, the model even comprises a covariant and local subnet of operators localized in bounded subsets of Minkowski space which has a nontrivial scattering matrix. The model thus exemplifies the algebraic construction of local observables from algebras associated with nonlocal fields.Comment: paper re-written with a change of emphasis and new result

A sharpened nuclearity condition for massless fields

A recently proposed phase space condition which comprises information about the vacuum structure and timelike asymptotic behavior of physical states is verified in massless free field theory. There follow interesting conclusions about the momentum transfer of local operators in this model.Comment: 13 pages, LaTeX. As appeared in Letters in Mathematical Physic

Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II

In the first part, we have constructed several families of interacting wedge-local nets of von Neumann algebras. In particular, there has been discovered a family of models based on the endomorphisms of the U(1)-current algebra of Longo-Witten. In this second part, we further investigate endomorphisms and interacting models. The key ingredient is the free massless fermionic net, which contains the U(1)-current net as the fixed point subnet with respect to the U(1) gauge action. Through the restriction to the subnet, we construct a new family of Longo-Witten endomorphisms on the U(1)-current net and accordingly interacting wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the structure of particle numbers and the S-matrices of the models constructed here do mix the spaces with different particle numbers of the bosonic Fock space.Comment: 33 pages, 1 tikz figure. The final version is available under Open Access. CC-B

An operator expansion for integrable quantum field theories

A large class of quantum field theories on 1+1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local observables in these models remains largely unknown. Aiming for more insight into their structure, we establish a series expansion for observables, similar but not identical to the well-known form factor expansion. This expansion will be the basis for a characterization and explicit construction of local observables, to be discussed elsewhere. Here, we establish the expansion independent of the localization aspect, and analyze its behavior under space-time symmetries. We also clarify relations with deformation methods in quantum field theory, specifically, with the warped convolution in the sense of Buchholz and Summers.Comment: minor corrections and clarifications, as published in J. Phys A; 24 page

Wedge-Local Quantum Fields and Noncommutative Minkowski Space

Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski spacetime, the consequences of the consistent application of the proper, untwisted Poincare group as the symmetry group are investigated. The emergent model contains an infinite family of fields which are labelled by different noncommutativity parameters, and related to each other by Lorentz transformations. The relative localization properties of these fields are investigated, and it is shown that to each field one can assign a wedge-shaped localization region of Minkowski space. This assignment is consistent with the principles of covariance and locality, i.e. fields localized in spacelike separated wedges commute. Regarding the model as a non-local, but wedge-local, quantum field theory on ordinary (commutative) Minkowski spacetime, it is possible to determine two-particle S-matrix elements, which turn out to be non-trivial. Some partial negative results concerning the existence of observables with sharper localization properties are also obtained.Comment: Version to appear in JHEP, 27 page

Asymptotic completeness in a class of massless relativistic quantum field theories

This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to Buchholz, is still valid under these weaker assumptions. The concepts of interaction and asymptotic completeness, provided by this theory, are adopted in the present investigation.Comment: 15 pages, LaTeX. As appeared in Communications in Mathematical Physic

Algebraic conformal quantum field theory in perspective

Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.Comment: Review paper, 40 pages. v2: minor changes and references added, so as to match published versio