6,042 research outputs found
Passive States for Essential Observers
The aim of this note is to present a unified approach to the results given in
\cite{bb99} and \cite{bs04} which also covers examples of models not presented
in these two papers (e.g. -dimensional Minkowski space-time for ).
Assuming that a state is passive for an observer travelling along certain
(essential) worldlines, we show that this state is invariant under the isometry
group, is a KMS-state for the observer at a temperature uniquely determined by
the structure constants of the Lie algebra involved and fulfills (a variant of)
the Reeh-Schlieder property. Also the modular objects associated to such a
state and the observable algebra of an observer are computed and a version of
weak locality is examined.Comment: 27 page
String-- and Brane--Localized Causal Fields in a Strongly Nonlocal Model
We study a weakly local, but nonlocal model in spacetime dimension
and prove that it is maximally nonlocal in a certain specific quantitative
sense. Nevertheless, depending on the number of dimensions , it has
string--localized or brane--localized operators which commute at spatial
distances. In two spacetime dimensions, the model even comprises a covariant
and local subnet of operators localized in bounded subsets of Minkowski space
which has a nontrivial scattering matrix. The model thus exemplifies the
algebraic construction of local observables from algebras associated with
nonlocal fields.Comment: paper re-written with a change of emphasis and new result
Magnetoconductance switching in an array of oval quantum dots
Employing oval shaped quantum billiards connected by quantum wires as the
building blocks of a linear quantum dot array, we calculate the ballistic
magnetoconductance in the linear response regime. Optimizing the geometry of
the billiards, we aim at a maximal finite- over zero-field ratio of the
magnetoconductance. This switching effect arises from a relative phase change
of scattering states in the oval quantum dot through the applied magnetic
field, which lifts a suppression of the transmission characteristic for a
certain range of geometry parameters. It is shown that a sustainable switching
ratio is reached for a very low field strength, which is multiplied by
connecting only a second dot to the single one. The impact of disorder is
addressed in the form of remote impurity scattering, which poses a temperature
dependent lower bound for the switching ratio, showing that this effect should
be readily observable in experiments.Comment: 11 pages, 8 figure
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
News from the Virasoro algebra
It is shown that the local quantum field theory of the chiral energy-
momentum tensor with central charge coincides with the gauge invariant
subtheory of the chiral current algebra at level 1, where the gauge
group is the global symmetry. At higher level, the same scheme gives
rise to -algebra extensions of the Virasoro algebra.Comment: 4 pages, Latex, DESY 93-11
Continuous Spectrum of Automorphism Groups and the Infraparticle Problem
This paper presents a general framework for a refined spectral analysis of a
group of isometries acting on a Banach space, which extends the spectral theory
of Arveson. The concept of continuous Arveson spectrum is introduced and the
corresponding spectral subspace is defined. The absolutely continuous and
singular-continuous parts of this spectrum are specified. Conditions are given,
in terms of the transposed action of the group of isometries, which guarantee
that the pure-point and continuous subspaces span the entire Banach space. In
the case of a unitarily implemented group of automorphisms, acting on a
-algebra, relations between the continuous spectrum of the automorphisms
and the spectrum of the implementing group of unitaries are found. The group of
spacetime translation automorphisms in quantum field theory is analyzed in
detail. In particular, it is shown that the structure of its continuous
spectrum is relevant to the problem of existence of (infra-)particles in a
given theory.Comment: 31 pages, LaTeX. As appeared in Communications in Mathematical
Physic
Comment on: Modular Theory and Geometry
In this note we comment on part of a recent article by B. Schroer and H.-W.
Wiesbrock. Therein they calculate some new modular structure for the
U(1)-current-algebra (Weyl-algebra). We point out that their findings are true
in a more general setting. The split-property allows an extension to
doubly-localized algebras.Comment: 13 pages, corrected versio
Towards a construction of inclusive collision cross-sections in the massless Nelson model
The conventional approach to the infrared problem in perturbative quantum
electrodynamics relies on the concept of inclusive collision cross-sections. A
non-perturbative variant of this notion was introduced in algebraic quantum
field theory. Relying on these insights, we take first steps towards a
non-perturbative construction of inclusive collision cross-sections in the
massless Nelson model. We show that our proposal is consistent with the
standard scattering theory in the absence of the infrared problem and discuss
its status in the infrared-singular case.Comment: 23 pages, LaTeX. As appeared in Ann. Henri Poincar\'
- …