Spacelike localization of long-range fields in a model of asymptotic electrodynamics

A previously proposed algebra of asymptotic fields in quantum electrodynamics is formulated as a net of algebras localized in regions which in general have unbounded spacelike extension. Electromagnetic fields may be localized in `symmetrical spacelike cones', but there are strong indications this is not possible in the present model for charged fields, which have tails extending in all space directions. Nevertheless, products of appropriately `dressed' fermion fields (with compensating charges) yield bi-localized observables.Comment: 29 pages, accepted for publication in Annales Henri Poincar\'

Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties

If a state is passive for uniformly accelerated observers in n-dimensional anti-de Sitter space-time (i.e. cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a "geodesic causal structure" on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded spacetime regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space-time localization. Examples are provided of models satisfying the hypotheses of these theorems.Comment: 27 pages, 1 figure: dedicated to Jacques Bros on the occasion of his 70th birthday. Revised version: typos corrected; as to appear in J. Math. Phy

Current trends in axiomatic quantum field theory

In this article a non--technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras of observables, their relation to the underlying fields and the significance of their relative positions. Moreover, the physical interpretation of the theory is discussed with emphasis on problems appearing in gauge theories, such as the revision of the particle concept, the determination of symmetries and statistics from the superselection structure, the analysis of the short distance properties and the specific features of relativistic thermal states. Some problems appearing in quantum field theory on curved spacetimes are also briefly mentioned. (Talk given at Ringberg Symposium on Quantum Field Theory, Ringberg Castle, June 1998

Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II

In the first part, we have constructed several families of interacting wedge-local nets of von Neumann algebras. In particular, there has been discovered a family of models based on the endomorphisms of the U(1)-current algebra of Longo-Witten. In this second part, we further investigate endomorphisms and interacting models. The key ingredient is the free massless fermionic net, which contains the U(1)-current net as the fixed point subnet with respect to the U(1) gauge action. Through the restriction to the subnet, we construct a new family of Longo-Witten endomorphisms on the U(1)-current net and accordingly interacting wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the structure of particle numbers and the S-matrices of the models constructed here do mix the spaces with different particle numbers of the bosonic Fock space.Comment: 33 pages, 1 tikz figure. The final version is available under Open Access. CC-B

On the Existence of Local Observables in Theories With a Factorizing S-Matrix

A recently proposed criterion for the existence of local quantum fields with a prescribed factorizing scattering matrix is verified in a non-trivial model, thereby establishing a new constructive approach to quantum field theory in a particular example. The existence proof is accomplished by analyzing nuclearity properties of certain specific subsets of Fermionic Fock spaces.Comment: 13 pages, no figures, comment in sect. 3 adde

The Quest for Understanding in Relativistic Quantum Physics

We discuss the status and some perspectives of relativistic quantum physics.Comment: Invited contribution to the Special Issue 2000 of the Journal of Mathematical Physics, 38 pages, typos corrected and references added, as to appear in JM

On the equivalence of two deformation schemes in quantum field theory

Two recent deformation schemes for quantum field theories on the two-dimensional Minkowski space, making use of deformed field operators and Longo-Witten endomorphisms, respectively, are shown to be equivalent.Comment: 14 pages, no figure. The final version is available under Open Access. CC-B