Operator product expansions as a consequence of phase space properties

The paper presents a model-independent, nonperturbative proof of operator product expansions in quantum field theory. As an input, a recently proposed phase space condition is used that allows a precise description of point field structures. Based on the product expansions, we also define and analyze normal products (in the sense of Zimmermann).Comment: v3: minor wording changes, as to appear in J. Math. Phys.; 12 page

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

Scaling algebras and pointlike fields: A nonperturbative approach to renormalization

We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a naturally defined scaling limit in the sense of Buchholz and Verch; we investigate the effect of this limit on the pointlike fields. Both for the fields and their operator product expansions, a well-defined limit procedure can be established. This can always be interpreted in the usual sense of multiplicative renormalization, where the renormalization factors are determined by our analysis. We also consider the limits of symmetry actions. In particular, for suitable limit states, the group of scaling transformations induces a dilation symmetry in the limit theory.Comment: minor changes and clarifications; as to appear in Commun. Math. Phys.; 37 page

Quantum backflow and scattering

Backflow is the phenomenon that the probability current of a quantum particle on the line can flow in the direction opposite to its momentum. In this article, previous investigations of backflow, pertaining to interaction-free dynamics or purely kinematical aspects, are extended to scattering situations in short-range potentials. It is shown that backflow is a universal quantum effect which exists in any such potential, and is always of bounded spatial extent in a specific sense. The effects of reflection and transmission processes on backflow are investigated, both analytically for general potentials, and numerically in various concrete examples

Scaling limits of integrable quantum field theories

Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is shown that massless scaling limit theories exist, and decompose into (twisted) tensor products of chiral, translation-dilation covariant field theories. On the subspace which is generated from the vacuum by the observables localized in finite light ray intervals, this symmetry can be extended to the M\"obius group. The structure of the interval-localized algebras in the chiral models is discussed in two explicit examples.Comment: Revised version: erased typos, improved formulations, and corrections of Lemma 4.8/Prop. 4.9. As published in RMP. 43 pages, 1 figur

Coincidence Arrangements of Local Observables and Uniqueness of the Vacuum in QFT

A new phase space criterion, encoding the physically motivated behavior of coincidence arrangements of local observables, is proposed in this work. This condition entails, in particular, uniqueness and purity of the energetically accessible vacuum states. It is shown that the qualitative part of this new criterion is equivalent to a compactness condition proposed in the literature. Its novel quantitative part is verified in massive free field theory.Comment: 27 pages, LaTe

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