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

On the status of pointlike fields in integrable QFTs

In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their n-point functions is unclear in this setting. An alternative approach uses fully convergent expressions for fields with weaker localization properties in spacelike wedges, and deduces existence of observables in bounded regions from there, but yields little information about their explicit form. We propose a new, hybrid construction: We aim to describe pointlike local quantum fields; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we establish them as closed operators affiliated with a net of local von Neumann algebras that is known from the wedge-local approach. This is shown to work at least in the Ising model

Energy inequalities in interacting quantum field theories

The classical energy conditions, originally motivated by the Penrose-Hawking singularity theorems of general relativity, are violated by quantum fields. A reminiscent notion of such conditions are the so called quantum energy inequalities (QEIs), which are however not known to hold generally in quantum field theory. Here we present first steps towards investigating QEIs in quantum field theories with self-interaction.Comment: to appear in the proceedings of the conference "Progress and Visions in Quantum Theory in View of Gravity - Bridging Foundations of Physics and Mathematics", Leipzig 2018; 8 page

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

A novel computational approach for predicting complex phenotypes in Drosophila (starvation-sensitive and sterile) by deriving their gene expression signatures from public data

Many research teams perform numerous genetic, transcriptomic, proteomic and other types of omic experiments to understand molecular, cellular and physiological mechanisms of disease and health. Often (but not always), the results of these experiments are deposited in publicly available repository databases. These data records often include phenotypic characteristics following genetic and environmental perturbations, with the aim of discovering underlying molecular mechanisms leading to the phenotypic responses. A constrained set of phenotypic characteristics is usually recorded and these are mostly hypothesis driven of possible to record within financial or practical constraints. We present a novel proof-of-principal computational approach for combining publicly available gene-expression data from control/mutant animal experiments that exhibit a particular phenotype, and we use this approach to predict unobserved phenotypic characteristics in new experiments (data derived from EBI’s ArrayExpress and ExpressionAtlas respectively). We utilised available microarray gene-expression data for two phenotypes (starvation-sensitive and sterile) in Drosophila. The data were combined using a linear-mixed effects model with the inclusion of consecutive principal components to account for variability between experiments in conjunction with Gene Ontology enrichment analysis. We present how available data can be ranked in accordance to a phenotypic likelihood of exhibiting these two phenotypes using random forest. The results from our study show that it is possible to integrate seemingly different gene-expression microarray data and predict a potential phenotypic manifestation with a relatively high degree of confidence (>80% AUC). This provides thus far unexplored opportunities for inferring unknown and unbiased phenotypic characteristics from already performed experiments, in order to identify studies for future analyses. Molecular mechanisms associated with gene and environment perturbations are intrinsically linked and give rise to a variety of phenotypic manifestations. Therefore, unravelling the phenotypic spectrum can help to gain insights into disease mechanisms associated with gene and environmental perturbations. Our approach uses public data that are set to increase in volume, thus providing value for money

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

On dilation symmetries arising from scaling limits

Quantum field theories, at short scales, can be approximated by a scaling limit theory. In this approximation, an additional symmetry is gained, namely dilation covariance. To understand the structure of this dilation symmetry, we investigate it in a nonperturbative, model independent context. To that end, it turns out to be necessary to consider non-pure vacuum states in the limit. These can be decomposed into an integral of pure states; we investigate how the symmetries and observables of the theory behave under this decomposition. In particular, we consider several natural conditions of increasing strength that yield restrictions on the decomposed dilation symmetry.Comment: 40 pages, 1 figur

Causality and dispersion relations and the role of the S-matrix in the ongoing research

The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their serious shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property requires the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These new concepts, which combine localization, vacuum polarization and thermal properties under the roof of modular theory, will be explained and their potential use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role but, different from Heisenberg's and Mandelstam's proposals, the new project is not a pure S-matrix approach. The S-matrix plays a new role as a "relative modular invariant"..Comment: 47 pages expansion of arguments and addition of references, corrections of misprints and bad formulation

Continuous Spectrum of Automorphism Groups and the Infraparticle Problem

This paper presents a general framework for a refined spectral analysis of a group of isometries acting on a Banach space, which extends the spectral theory of Arveson. The concept of continuous Arveson spectrum is introduced and the corresponding spectral subspace is defined. The absolutely continuous and singular-continuous parts of this spectrum are specified. Conditions are given, in terms of the transposed action of the group of isometries, which guarantee that the pure-point and continuous subspaces span the entire Banach space. In the case of a unitarily implemented group of automorphisms, acting on a $C^*$-algebra, relations between the continuous spectrum of the automorphisms and the spectrum of the implementing group of unitaries are found. The group of spacetime translation automorphisms in quantum field theory is analyzed in detail. In particular, it is shown that the structure of its continuous spectrum is relevant to the problem of existence of (infra-)particles in a given theory.Comment: 31 pages, LaTeX. As appeared in Communications in Mathematical Physic

Global bundle adjustment with variable orientation point distance for precise mars express orbit reconstruction

The photogrammetric bundle adjustment of line scanner image data requires a precise description of the time-dependent image orientation. For this task exterior orientation parameters of discrete points are used to model position and viewing direction of a camera trajectory via polynomials. This paper investigates the influence of the distance between these orientation points on the quality of trajectory modeling. A new method adapts the distance along the trajectory to the available image information. Compared to a constant distance as used previously, a better reconstruction of the exterior orientation is possible, especially when image quality changes within a strip. In our research we use image strips of the High Resolution Stereo Camera (HRSC), taken to map the Martian surface. Several experiments on the global image data set have been carried out to investigate how the bundle adjustment improves the image orientation, if the new method is employed. For evaluation the forward intersection errors of 3D points derived from HRSC images, as well as their remaining height differences to the MOLA DTM are used. In 13.5 % (515 of 3,828) of the image strips, taken during this ongoing mission over the last 12 years, high frequency image distortions were found. Bundle adjustment with a constant orientation point distance was able to reconstruct the orbit in 239 (46.4 %) cases. A variable orientation point distance increased this number to 507 (98.6 %).German Federal Ministry for Economic Affairs and Energy (BMWi)German Aerospace Center (DLR)/50 QM 130