It is emphasized that for interactions with derivative couplings, the Ward Identity (WI) securing the preservation of a global U(1) symmetry should be modified. Scalar QED is taken as an explicit example. More precisely, it is rigorously shown in sca
lar QED that the naive WI and the improved Ward Identity (Master Ward Identity, MWI) are related to each other by a finite renormalization of the time-ordered product (T-product) for the derivative fields; and we point out that the MWI has advantages over the naive WI - in particular with regard to the proof of the MWI. We show that the MWI can be fulfilled in all orders of perturbation theory by an appropriate renormalization of the T-product, without conflict with other standard renormalization conditions. Relations with other recent formulations of the MWI are established.
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.
In contrast to Hamiltonian perturbation theory which changes the time evolution, spacelike deformations proceed by changing the translations (momentum operators). The free Maxwell theory is only the first member of an infinite family of spacelike def
ormations of the complex massless Klein-Gordon quantum field into fields of higher helicity. A similar but simpler instance of spacelike deformation allows to increase the mass of scalar fields.
String-localized quantum fields transforming in Wigners infinite-spin representations were introduced by Mund, Schroer and Yngvason. We construct these fields as limits of fields of finite mass $mto 0$ and finite spin $stoinfty$. We determine a strin
g-localized infinite-spin quantum stress-energy tensor with a novel prescription that does not refer to a classical Lagrangean.
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 $m to 0$.
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.
We review the definition of hypergroups by Sunder, and we associate a hypergroup to a type III subfactor $Nsubset M$ of finite index, whose canonical endomorphism $gammainmathrm{End}(M)$ is multiplicity-free. It is realized by positive maps of $M$ th
at have $N$ as fixed points. If the depth is $>2$, this hypergroup is different from the hypergroup associated with the fusion algebra of $M$-$M$ bimodules that was Sunders original motivation to introduce hypergroups. We explain how the present hypergroup, associated with a suitable subfactor, controls the composition of transparent boundary conditions between two isomorphic quantum field theories, and that this generalizes to a hypergroupoid of boundary conditions between different quantum field theories sharing a common subtheory.
We give a proof of a formula for the trace of self-braidings (in an arbitrary channel) in UMTCs which first appeared in the context of rational conformal field theories (CFTs). The trace is another invariant for UMTCs which depends only on modular da
ta, and contains the expression of the Frobenius-Schur indicator as a special case. Furthermore, we discuss some applications of the trace formula to the realizability problem of modular data and to the classification of UMTCs.
Boundary conditions in relativistic QFT can be classified by deep results in the theory of braided or modular tensor categories.
