83 research outputs found

### Looking beyond the Thermal Horizon: Hidden Symmetries in Chiral Models

In thermal states of chiral theories, as recently investigated by H.-J.
Borchers and J. Yngvason, there exists a rich group of hidden symmetries. Here
we show that this leads to a radical converse of of the Hawking-Unruh
observation in the following sense. The algebraic commutant of the algebra
associated with a (heat bath) thermal chiral system can be used to reprocess
the thermal system into a ground state system on a larger algebra with a larger
localization space-time. This happens in such a way that the original system
appears as a kind of generalized Unruh restriction of the ground state sytem
and the thermal commutant as being transmutated into newly created ``virgin
space-time region'' behind a horizon. The related concepts of a ``chiral
conformal core'' and the possibility of a ``blow-up'' of the latter suggest
interesting ideas on localization of degrees of freedom with possible
repercussion on how to define quantum entropy of localized matter content in
Local Quantum Physics.Comment: 17 pages, tcilatex, still more typos removed and one reference
correcte

### Modular Groups of Quantum Fields in Thermal States

For a quantum field in a thermal equilibrium state we discuss the group
generated by time translations and the modular action associated with an
algebra invariant under half-sided translations. The modular flows associated
with the algebras of the forward light cone and a space-like wedge admit a
simple geometric description in two dimensional models that factorize in
light-cone coordinates. At large distances from the domain boundary compared to
the inverse temperature the flow pattern is essentially the same as time
translations, whereas the zero temperature results are approximately reproduced
close to the edge of the wedge and the apex of the cone. Associated with each
domain there is also a one parameter group with a positive generator, for which
the thermal state is a ground state. Formally, this may be regarded as a
certain converse of the Unruh-effect.Comment: 28 pages, 4 figure

### 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

### Endomorphism Semigroups and Lightlike Translations

Certain criteria are demonstrated for a spatial derivation of a von Neumann
algebra to generate a one-parameter semigroup of endomorphisms of that algebra.
These are then used to establish a converse to recent results of Borchers and
of Wiesbrock on certain one-parameter semigroups of endomorphisms of von
Neumann algebras (specifically, Type III_1 factors) that appear as lightlike
translations in the theory of algebras of local observables.Comment: 9 pages, Late

### 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

### How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential

The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system

### Anomalous Scale Dimensions from Timelike Braiding

Using the previously gained insight about the particle/field relation in
conformal quantum field theories which required interactions to be related to
the existence of particle-like states associated with fields of anomalous
scaling dimensions, we set out to construct a classification theory for the
spectra of anomalous dimensions. Starting from the old observations on
conformal superselection sectors related to the anomalous dimensions via the
phases which appear in the spectral decomposition of the center of the
conformal covering group $Z(\widetilde{SO(d,2)}),$ we explore the possibility
of a timelike braiding structure consistent with the timelike ordering which
refines and explains the central decomposition. We regard this as a preparatory
step in a new construction attempt of interacting conformal quantum field
theories in D=4 spacetime dimensions. Other ideas of constructions based on the
$AdS_{5}$-$CQFT_{4}$ or the perturbative SYM approach in their relation to the
present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages
tcilatex, 3 latexcad figure

### Pauli problem for a spin of arbitrary length: A simple method to determine its wave function

The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and the experimental setup is elementary. Other approaches to determine state vectors from measurements, also known as the ‘‘Pauli problem,’’ are reviewed for both spin and particle systems

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