2,632 research outputs found
Translocality and a Duality Principle in Generally Covariant Quantum Field Theory
It is argued that the formal rules of correspondence between local
observation procedures and observables do not exhaust the entire physical
content of generally covariant quantum field theory. This result is obtained by
expressing the distinguishing features of the local kinematical structure of
quantum field theory in the generally covariant context in terms of a
translocal structure which carries the totality of the nonlocal kinematical
informations in a local region. This gives rise to a duality principle at the
dynamical level which emphasizes the significance of the underlying translocal
structure for modelling a minimal algebra around a given point. We discuss the
emergence of classical properties from this point of view.Comment: 12 pages. To appear in Classical Quantum Gravit
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
Dynamical mapping method in nonrelativistic models of quantum field theory
The solutions of Heisenberg equations and two-particles eigenvalue problems
for nonrelativistic models of current-current fermion interaction and model are obtained in the frameworks of dynamical mapping method. The
equivalence of different types of dynamical mapping is shown. The connection
between renormalization procedure and theory of selfadjoint extensions is
elucidated.Comment: 14 page
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
Scattering States of Plektons (PARTICLES with Braid Group Statistics) in 2+1 Dimensional Quantum Field Theory
A Haag-Ruelle scattering theory for particles with braid group statistics is
developed, and the arising structure of the Hilbert space of multiparticle
states is analyzed.Comment: 18 pages, LATEX, DAMTP-94-9
Localized Endomorphisms of the Chiral Ising Model
Based on the treatment of the chiral Ising model by Mack and Schomerus, we
present examples of localized endomorphisms and
. It is shown that they lead to the same
superselection sectors as the global ones in the sense that unitary equivalence
and holds. Araki's formalism of the selfdual CAR algebra is
used for the proof. We prove local normality and extend representations and
localized endomorphisms to a global algebra of observables which is generated
by local von Neumann algebras on the punctured circle. In this framework, we
manifestly prove fusion rules and derive statistics operators.Comment: 41 pages, latex2
Nonlinear Schr\"odinger equation for a PT symmetric delta-functions double well
The time-independent nonlinear Schr\"odinger equation is solved for two
attractive delta-function shaped potential wells where an imaginary loss term
is added in one well, and a gain term of the same size but with opposite sign
in the other. We show that for vanishing nonlinearity the model captures all
the features known from studies of PT symmetric optical wave guides, e.g., the
coalescence of modes in an exceptional point at a critical value of the
loss/gain parameter, and the breaking of PT symmetry beyond. With the
nonlinearity present, the equation is a model for a Bose-Einstein condensate
with loss and gain in a double well potential. We find that the nonlinear
Hamiltonian picks as stationary eigenstates exactly such solutions which render
the nonlinear Hamiltonian itself PT symmetric, but observe coalescence and
bifurcation scenarios different from those known from linear PT symmetric
Hamiltonians.Comment: 16 pages, 9 figures, to be published in Journal of Physics
Vacuum Structures in Hamiltonian Light-Front Dynamics
Hamiltonian light-front dynamics of quantum fields may provide a useful
approach to systematic non-perturbative approximations to quantum field
theories. We investigate inequivalent Hilbert-space representations of the
light-front field algebra in which the stability group of the light-front is
implemented by unitary transformations. The Hilbert space representation of
states is generated by the operator algebra from the vacuum state. There is a
large class of vacuum states besides the Fock vacuum which meet all the
invariance requirements. The light-front Hamiltonian must annihilate the vacuum
and have a positive spectrum. We exhibit relations of the Hamiltonian to the
nontrivial vacuum structure.Comment: 16 pages, report \# ANL-PHY-7524-TH-93, (Latex
Neural Action Fields for Optic Flow Based Navigation: A Simulation Study of the Fly Lobula Plate Network
Optic flow based navigation is a fundamental way of visual course control described in many different species including man. In the fly, an essential part of optic flow analysis is performed in the lobula plate, a retinotopic map of motion in the environment. There, the so-called lobula plate tangential cells possess large receptive fields with different preferred directions in different parts of the visual field. Previous studies demonstrated an extensive connectivity between different tangential cells, providing, in principle, the structural basis for their large and complex receptive fields. We present a network simulation of the tangential cells, comprising most of the neurons studied so far (22 on each hemisphere) with all the known connectivity between them. On their dendrite, model neurons receive input from a retinotopic array of Reichardt-type motion detectors. Model neurons exhibit receptive fields much like their natural counterparts, demonstrating that the connectivity between the lobula plate tangential cells indeed can account for their complex receptive field structure. We describe the tuning of a model neuron to particular types of ego-motion (rotation as well as translation around/along a given body axis) by its ‘action field’. As we show for model neurons of the vertical system (VS-cells), each of them displays a different type of action field, i.e., responds maximally when the fly is rotating around a particular body axis. However, the tuning width of the rotational action fields is relatively broad, comparable to the one with dendritic input only. The additional intra-lobula-plate connectivity mainly reduces their translational action field amplitude, i.e., their sensitivity to translational movements along any body axis of the fly
The second law of thermodynamics, TCP, and Einstein causality in anti-de Sitter space-time
If the vacuum is passive for uniformly accelerated observers in 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 Hawking-Unruh
temperature, (b) discover a TCP symmetry, and (c) find that observables in
complementary wedge-shaped regions are commensurable (local) in the vacuum
state. These results are model independent and hold in any theory which is
compatible with some weak notion of space-time localization.Comment: 8 pages, slightly improved results, minor changes in the expository
part, new title; to appear in "Classical and Quantum Gravity
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