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A non-perturbative and exactly solvable quantum field theoretical model for a "dressed Dirac field" is presented, that exhibits all the kinematical features of QED: an appropriate delocalization of the charged field as a prerequisite for the global Gauss Law, superselected photon clouds (asymptotic expectation values of the Maxwell field), infraparticle nature of charged particles that cannot be separated from their photon clouds, broken Lorentz symmetry. The model serves as an intermediate leg on a new roadmap towards full QED, formulated as an off-shell theory, i.e., including a perturbative construction of its interacting charged fields. It also fills a gap in recent discussions of the "Infrared Triangle", and points the way towards a new scattering theory for theories with massless particles of helicity $\geq 1$, in which infraparticles can be described at the level of charged fields, rather than just states., Comment: v1: 58 pages, 2 figures. v2: presentation improved and extended (notably Sect. 4), references added

We establish the Haag–Kastler axioms for a class of interacting quantum field theories on the two-dimensional de Sitter space, which satisfy finite speed of light. The $${\mathscr {P}} (\varphi )_2$$ model constructed in [3], describing massive scalar bosons with polynomial interactions, provides an example.

We show how chirality of the weak interactions stems from string independence in the string-local formalism of quantum field theory., Comment: Latex, 31 pages. v2: minor changes, 3 references added, author order now alphabetical. v3: substantial rewrite to improve presentation, conclusions unchanged. v4: minor edits to match published version, one reference added. To appear in Annales Henri Poincar\'e

Massive and massless potentials play an essential role in the perturbative formulation of particle interactions. Many difficulties arise due to the indefinite metric in gauge theoretic approaches, or the increase with the spin of the UV dimension of massive potentials. All these problems can be evaded in one stroke: modify the potentials by suitable terms that leave unchanged the field strengths, but are not polynomial in the momenta. This feature implies a weaker localization property: the potentials are "string-localized". In this setting, several old issues can be solved directly in the physical Hilbert space of the respective particles: We can control the separation of helicities in the massless limit of higher spin fields and conversely we recover massive potentials with 2s+1 degrees of freedom by a smooth deformation of the massless potentials ("fattening"). We construct stress-energy tensors for massless fields of any helicity (thus evading the Weinberg-Witten theorem). We arrive at a simple understanding of the van Dam-Veltman-Zakharov discontinuity concerning, e.g., the distinction between a massless or a very light graviton. Finally, the use of string-localized fields opens new perspectives for interacting quantum field theories with, e.g., vector bosons or gravitons., Comment: 30 pages. v4: As published. v3: Introduction completely rewritten; more quantitative treatment of the DVZ issue; references and comments added. v2: Deleted a passage erroneously claimed to be "unknown" in the appendix. An abridged version is arXiv:1703.04408

We present the ${\mathscr P}(\varphi)_2$ model on de Sitter space in the canonical formulation. We discuss the role of the Noether theorem and we provide explicit expressions for the energy-stress tensor of the interacting model., Comment: minor corrections

It is well-known that a (point-localized) free quantum field for massive particles with spin $s$ acting in a Hilbert space has at best scaling dimension $s+1$, which excludes its use in the perturbative construction of renormalizable interacting models for higher spin ($s\geq 1$). Up to date, such models have been constructed only in the context of gauge theory, at the cost of introducing additional unphysical (ghost) fields and an unphysical (indefinite metric) state space. The unphysical degrees of freedom are divided out by requiring gauge (or BRST) invariance. We construct free quantum fields for higher spin particles which have the same good UV behaviour as the scalar field (scaling dimension one), and at the same time act on a Hilbert space without ghosts. They are localized on semi-infinite strings extending to space-like infinity, but are linearly related to their point-local counterparts. We argue that this is sufficient locality for a perturbative construction of interacting models of the gauge theory type, with a string-independent S-matrix and point-localized interacting observable fields. The usual principle of gauge-invariance is here replaced by the (deeper) principle of locality., Comment: 38 pages. Minor modifications; references added

Correction to: Ann. Henri Poincar ́e 19 (2018), 843–874https://doi.org/10.1007/s00023-017-0637-3 Universidad de Costa Rica/[820-B8-225]/UCR/Costa Rica UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemática UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de investigaciones Matemáticas y Metamatemáticas (CIMM)

For a renormalizability proof of perturbative models in the Epstein--Glaser scheme with string-localized quantum fields, one needs to know what freedom one has in the definition of time-ordered products of the interaction Lagrangian. This paper provides a first step in that direction. The basic issue is the presence of an open set of $n$-tuples of strings which cannot be chronologically ordered. We resolve it by showing that almost all such string configurations can be dissected into finitely many pieces which can indeed be chronologically ordered. This fixes the time-ordered products of linear field factors outside a nullset of string configurations. (The extension across the nullset, as well as the definition of time-ordered products of Wick monomials, will be discussed elsewhere.), 23 pages, 4 figures

The problem of accounting for the quantum degrees of freedom in passing from massive higher-spin potentials to massless ones and its inverse, the "fattening" of massless tensor potentials of helicity $\pm h$ to their massive $s = |h|$ counterparts, are solved - in a perfectly ghost-free approach - using "string-localized fields". This approach allows to overcome the Weinberg-Witten impediment against the existence of massless $|h| \geq 2$ energy-momentum tensors, and to qualitatively and quantitatively resolve the van Dam-Veltman-Zakharov discontinuity concerning, e.g., very light gravitons, in the limit $m \to 0$., Comment: v3: Final version as to appear in Phys.Lett.B. This is an abridged version of arXiv:1703.04407

Borchers has shown that in a translation covariant vacuum representation of a theory of local observables with positive energy the following holds: The (Tomita) modular objects associated with the observable algebra of a fixed wedge region give rise to a representation of the subgroup of the Poincare group generated by the boosts and the reflection associated to the wedge, and the translations. We prove here that Borchers' theorem also holds in charged sectors with (possibly non-Abelian) braid group statistics in low space-time dimensions. Our result is a crucial step towards the Bisognano-Wichmann theorem for Plektons in d=3, namely that the mentioned modular objects generate a representation of the proper Poincare group, including a CPT operator. Our main assumptions are Haag duality of the observable algebra, and translation covariance with positive energy as well as finite statistics of the sector under consideration., 15 pages

It is shown that the l1-distance in the space of probability assignments on a finite set Ω provides a criterion to judge whether two assignments are too close to each other to be distinguished by a statistical test. The criterion is independent of the number of elements of Ω. Other notions of distance are also discussed.

In contrast to the usual representations of of the Poincar\'e group of finite spin or helicity the Wigner representations of mass zero and infinite spin are known to be incompatible with pointlike localized quantum fields. We present here a construction of quantum fields associated with these representations that are localized in semi-infinite, space-like strings. The construction is based on concepts outside the realm of Lagrangian quantization with the potential for further applications., Comment: References, some text and an appendix added

The geometric action of modular groups for wedge regions (Bisognano-Wichmann property) is derived from the principles of local quantum physics for a large class of Poincare covariant models in d=4. As a consequence, the CPT theorem holds for this class. The models must have a complete interpretation in terms of massive particles. The corresponding charges need not be localizable in compact regions: The most general case is admitted, namely localization in spacelike cones., Comment: 16 pages; improved and corrected formulations

We show that a quantum field theoretic model of anyons cannot be ‘free’ in the restrictive sense that the basic fields create only one-particle states out of the vacuum.

It is shown that particles with braid group statistics (Plektons) in three-dimensional space-time cannot be free, in a quite elementary sense: They must exhibit elastic two-particle scattering into every solid angle, and at every energy. This also implies that for such particles there cannot be any operators localized in wedge regions which create only single particle states from the vacuum and which are well-behaved under the space-time translations (so-called temperate polarization-free generators). These results considerably strengthen an earlier "NoGo-theorem for 'free' relativistic Anyons". As a by-product we extend a fact which is well-known in quantum field theory to the case of topological charges (i.e., charges localized in space-like cones) in d>3, namely: If there is no elastic two-particle scattering into some arbitrarily small open solid angle element, then the 2-particle S-matrix is trivial., 25 pages, 4 figures. Comment on model-building added in the introduction

We consider a purely massive local relativistic quantum theory specified by a family of von Neumann algebras indexed by the space-time regions. We assume that, affiliated with the algebras associated to wedge regions, there are operators which create only single particle states from the vacuum (so-called polarization-free generators) and are well-behaved under the space-time translations. Strengthening a result of Borchers, Buchholz and Schroer, we show that then the theory is unitarily equivalent to that of a free field for the corresponding particle type. We admit particles with any spin and localization of the charge in space-like cones, thereby covering the case of string-localized covariant quantum fields., 21 pages. The second (and crucial) hypothesis of the theorem has been relaxed and clarified, thanks to the stimulus of an anonymous referee. (The polarization-free generators associated with wedge regions, which always exist, are assumed to be temperate.)

We prove the Bisognano-Wichmann and CPT theorems for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory, assuming Poincare covariance and asymptotic completeness. The particle masses must be isolated points in the mass spectra of the corresponding charged sectors, and may only be finitely degenerate., Comment: 35 pages, 2 figures. References added; minor re-organization

We prove the spin-statistics theorem for massive particles obeying braid group statistics in three-dimensional Minkowski space. We start from first principles of local relativistic quantum theory. The only assumption is a gap in the mass spectrum of the corresponding charged sector, and a restriction on the degeneracy of the corresponding mass., Comment: 21 pages, 2 figures. Citation added; Minor modifications of Appendix A

We present a construction of string-localized covariant free quantum fields for a large class of irreducible (ray) representations of the Poincare group. Among these are the representations of mass zero and infinite spin, which are known to be incompatible with point-like localized fields. (Based on joint work with B. Schroer and J. Yngvason [13].)

We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincar\'e group and localized in semi-infinite strings extending to spacelike infinity. Among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point-like localized fields. For the massive representation and the massless representations of finite helicity, all string-localized free fields can be written as an integral, along the string, of point-localized tensor or spinor fields. As a special case we discuss the string-localized vector fields associated with the point-like electromagnetic field and their relation to the axial gauge condition in the usual setting., Comment: minor corrections

Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language., Comment: 1 figure

We discuss a concept of particle localization which is motivated from quantum field theory, and has been proposed by Brunetti, Guido and Longo and by Schroer. It endows the single particle Hilbert space with a family of real subspaces indexed by the space-time regions, with certain specific properties reflecting the principles of locality and covariance. We show by construction that such a localization structure exists also in the case of massive anyons in d=2+1, i.e. for particles with positive mass and with arbitrary spin s in the reals. The construction is completely intrinsic to the corresponding ray representation of the (proper orthochronous) Poincare group. Our result is of particular interest since there are no free fields for anyons, which would fix a localization structure in a straightforward way. We present explicit formulas for the real subspaces, expected to turn out useful for the construction of a quantum field theory for anyons. In accord with well-known results, only localization in string-like, instead of point-like or bounded, regions is achieved. We also prove a single-particle PCT theorem, exhibiting a PCT operator which acts geometrically correctly on the family of real subspaces., Comment: 31 pages, 1 figure. Minor changes to conform with J. Math. Phys. version

We propose a canonical description of the dynamics of quantum systems on a class of Robertson-Walker space-times. We show that the worldline of an observer in such space-times determines a unique orbit in the local conformal group SO(4,1) of the space-time and that this orbit determines a unique transport on the space-time. For a quantum system on the space-time modeled by a net of local algebras, the associated dynamics is expressed via a suitable family of ``propagators''. In the best of situations, this dynamics is covariant, but more typically the dynamics will be ``quasi-covariant'' in a sense we make precise. We then show by using our technique of ``transplanting'' states and nets of local algebras from de Sitter space to Robertson-Walker space that there exist quantum systems on Robertson-Walker spaces with quasi-covariant dynamics. The transplanted state is locally passive, in an appropriate sense, with respect to this dynamics., Comment: 21 pages, 1 figure