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Jens Mund

Publications and source records attributed to Jens Mund.

At least 19 recordsLinked to original sources
arXiv2022

How the Higgs potential got its shape

String-localized quantum field theory allows renormalizable couplings involving massive vector bosons, without invoking negative-norm states and compensating ghosts. We analyze the most general coupling of a massive vector boson to a scalar field, and find that the scalar field necessarily comes with a quartic potential which has the precise shape of the shifted Higgs potential. In other words: the shape of the Higgs potential has not to be assumed, but arises as a consistency condition among fundamental principles of QFT: Hilbert space, causality, and covariance. The consistency can be achieved by relaxing the localization properties of auxiliary quantities, including interacting charged fields, while observable fields and the S-matrix are not affected. This is an instance of the "L-V formalism" - a novel model-independent scheme that can be used as a tool to "renormalize the non-renormalizable" by adding a total derivative to the interaction.

hep-th↗
arXiv2021

Infraparticle quantum fields and the formation of photon clouds

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.

hep-th↗
arXiv2021

Revisiting the Okubo-Marshak argument

Modular localization and the theory of string-localized fields have revolutionized several key aspects of quantum field theory. They reinforce the contention that local symmetry emerges directly from quantum theory, but global gauge invariance remains in general an unwarranted assumption, to be examined case by case. Armed with those modern tools, we reconsider here the classical Okubo-Marshak argument on the non-existence of a "strong CP problem" in quantum chromodynamics.

hep-ph↗
arXiv2021

Interacting massless infraparticles in 1+1 dimensions

The Buchholz' scattering theory of waves in two dimensional massless models suggests a natural definition of a scattering amplitude. We compute such a scattering amplitude for charged infraparticles that live in the GNS representation of the 2$d$ massless scalar free field and obtain a non-trivial result. It turns out that these excitations exchange phases, depending on their charges, when they collide.

math-ph↗
arXiv2020

Gauss' Law and String-Localized Quantum Field Theory

The quantum Gauss Law as an interacting field equation is a prominent feature of QED with eminent impact on its algebraic and superselection structure. It forces charged particles to be accompanied by "photon clouds" that cannot be realized in the Fock space, and prevents them from having a sharp mass. Because it entails the possibility of "measurement of charges at a distance", it is well-known to be in conflict with locality of charged fields in a Hilbert space. We show how a new approach to QED advocated by the authors, that avoids indefinite metric and ghosts, can secure causality and achieve Gauss' Law along with all its nontrivial consequences. We explain why this is not at variance with recent results in a paper by Buchholz et al.

hep-th↗
arXiv2019

Interacting Quantum Fields on de Sitter Space

In 1975 Figari, Høegh-Krohn and Nappi constructed the P(phi)_2 model on the de Sitter space. Here we complement their work with new results, as well as by connecting this model to various areas of mathematics. In particular, i.) we discuss the causal structure of de Sitter space and the induces representations of the Lorentz group. We show that the UIRs of SO_0(1,2) for both the principal and the complementary series can be formulated on Hilbert spaces whose functions are supported on a Cauchy surface, ii.) we describe the free classical dynamical system in both its covariant and canonical form, and present the associated quantum one-particle KMS structures in the sense of Kay, iii.) we discuss the localisation properties of one-particle wave functions and how these properties are inherited by the algebras of local observables. In addition, we describe the relations between the modular objects (in the sense of Tomita-Takesaki theory) associated to wedge algebras and the representations of the Lorentz group, iv.) we connect the representations of SO(1,2) to unitary representations of SO(3) on the Euclidean sphere, and discuss how the P(phi)_2 interaction can be represented by a rotation invariant vector in the Euclidean Fock space. We present a novel Osterwalder-Schrader reconstruction theorem, which shows that physical infrared problems are absent on de Sitter space, v.) we explain how the generators of the boosts and the rotations for the interacting quantum field theory arise arise from the stress-energy tensor. Finally, we show that the interacting quantum fields satisfy the equations of motion in their covariant form. In summary, we argue that the de Sitter P(phi)_2 model is the simplest and most explicit relativistic quantum field theory, which satisfies basic expectations, like covariance, particle creation, stability and finite speed of light.

math-ph↗
arXiv2017

The chirality theorem

We show how chirality of the weak interactions stems from string independence in the string-local formalism of quantum field theory.

hep-th↗
arXiv2017

Helicity decoupling in the massless limit of massive tensor fields

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.

hep-th↗
arXiv2017

Relations between positivity, localization and degrees of freedom: the Weinberg-Witten theorem and the van Dam-Veltman-Zakharov discontinuity

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 $m \to 0$.

hep-th↗
arXiv2017

String chopping and time-ordered products of linear string-localized quantum fields

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.)

math-ph↗
arXiv2016

String-localized free vector and tensor potentials for massive particles with any spin: I. Bosons

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.

hep-th↗
arXiv2012

Braid group statistics implies scattering in three-dimensional local quantum physics

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.

hep-th↗
arXiv2012

An Algebraic Jost-Schroer Theorem for Massive Theories

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.

hep-th↗
arXiv2009

The CPT and Bisognano-Wichmann Theorems for Anyons and Plektons in d=2+1

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.

math-ph↗
arXiv2008

Borchers' Commutation Relations for Sectors with Braid Group Statistics in Low Dimensions

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.

math-ph↗