Local fields in boundary conformal QFT

Conformal field theory on the half-space x>0 of Minkowski space-time ("boundary CFT") is analyzed from an algebraic point of view, clarifying in particular the algebraic structure of local algebras and the bi-localized charge structure of local fields. The field content and the admissible boundary conditions are characterized in terms of a non-local chiral field algebra.Comment: 58 pages, 5 figures. v2: organization of results improved; version to appear in RM

Boundary Quantum Field Theory on the Interior of the Lorentz Hyperboloid

We construct local, boost covariant boundary QFT nets of von Neumann algebras on the interior of the Lorentz hyperboloid LH = {x^2 - t^2 > R^2, x>0}, in the two-dimensional Minkowski spacetime. Our first construction is canonical, starting with a local conformal net on the real line, and is analogous to our previous construction of local boundary CFT nets on the Minkowski half-space. This net is in a thermal state at Hawking temperature. Then, inspired by a recent construction by E. Witten and one of us, we consider a unitary semigroup that we use to build up infinitely many nets. Surprisingly, the one-particle semigroup is again isomorphic to the semigroup of symmetric inner functions of the disk. In particular, by considering the U(1)-current net, we can associate with any given symmetric inner function a local, boundary QFT net on LH. By considering different states, we shall also have nets in a ground state, rather than in a KMS state.Comment: 18 page

Spacelike deformations: Higher-helicity fields from scalar fields

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 deformations 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.Comment: v2: 18p, largely extended and more results added. Title adjuste

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 [7, 19]. 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 [3, 17]. We show how a new approach to QED advocated in [25, 26, 30, 31] 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 [8]

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 $m \to 0$.Comment: v3: Final version as to appear in Phys.Lett.B. This is an abridged version of arXiv:1703.0440

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.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:1703.0440