9,712 research outputs found
Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
Warped convolutions of operators were recently introduced in the algebraic
framework of quantum physics as a new constructive tool. It is shown here that
these convolutions provide isometric representations of Rieffel's strict
deformations of C*-dynamical systems with automorphic actions of R^n, whenever
the latter are presented in a covariant representation. Moreover, the device
can be used for the deformation of relativistic quantum field theories by
adjusting the convolutions to the geometry of Minkowski space. The resulting
deformed theories still comply with pertinent physical principles and their
Tomita-Takesaki modular data coincide with those of the undeformed theory; but
they are in general inequivalent to the undeformed theory and exhibit different
physical interpretations.Comment: 34 page
An Algebraic Characterization of Vacuum States in Minkowski Space. III. Reflection Maps
Employing the algebraic framework of local quantum physics, vacuum states in
Minkowski space are distinguished by a property of geometric modular action.
This property allows one to construct from any locally generated net of
observables and corresponding state a continuous unitary representation of the
proper Poincare group which acts covariantly on the net and leaves the state
invariant. The present results and methods substantially improve upon previous
work. In particular, the continuity properties of the representation are shown
to be a consequence of the net structure, and surmised cohomological problems
in the construction of the representation are resolved by demonstrating that,
for the Poincare group, continuous reflection maps are restrictions of
continuous homomorphisms.Comment: 20 pages; change of title, reference added; version as to appear in
Commun. Math. Phy
Geometric modular action and spontaneous symmetry breaking
We study spontaneous symmetry breaking for field algebras on Minkowski space
in the presence of a condition of geometric modular action (CGMA) proposed
earlier as a selection criterion for vacuum states on general space-times. We
show that any internal symmetry group must commute with the representation of
the Poincare group (whose existence is assured by the CGMA) and each
translation-invariant vector is also Poincare invariant. The subspace of these
vectors can be centrally decomposed into pure invariant states and the CGMA
holds in the resulting sectors. As positivity of the energy is not assumed,
similar results may be expected to hold for other space--times.Comment: Dedicated to the memory of Siegfried Schlieder. 17 pages, no figures.
Revised version: simplified arguments and improved results; as to appear in
Annales H. 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
Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools
We provide a brief overview of the basic tools and concepts of quantum field
theoretical scattering theory. This article is commissioned by the Encyclopedia
of Mathematical Physics, edited by J.-P. Francoise, G. Naber and T.S. Tsun, to
be published by the Elsevier publishing house.Comment: 14 pages, no figure
There are No Causality Problems for Fermi's Two Atom System
A repeatedly discussed gedanken experiment, proposed by Fermi to check
Einstein causality, is reconsidered. It is shown that, contrary to a recent
statement made by Hegerfeldt, there appears no causality paradoxon in a proper
theoretical description of the experiment.Comment: 6 pages, latex, DESY 94-02
Covariant and quasi-covariant quantum dynamics in Robertson-Walker space-times
We propose a canonical description of the dynamics of quantum systems on a
class of Robertson-Walker space-times. We show that the worldline of an
observer in such space-times determines a unique orbit in the local conformal
group SO(4,1) of the space-time and that this orbit determines a unique
transport on the space-time. For a quantum system on the space-time modeled by
a net of local algebras, the associated dynamics is expressed via a suitable
family of ``propagators''. In the best of situations, this dynamics is
covariant, but more typically the dynamics will be ``quasi-covariant'' in a
sense we make precise. We then show by using our technique of ``transplanting''
states and nets of local algebras from de Sitter space to Robertson-Walker
space that there exist quantum systems on Robertson-Walker spaces with
quasi-covariant dynamics. The transplanted state is locally passive, in an
appropriate sense, with respect to this dynamics.Comment: 21 pages, 1 figur
Quantum statistics and locality
It is shown that two observers have mutually commuting observables if they
are able to prepare in each subsector of their common state space some state
exhibiting no mutual correlations. This result establishes a heretofore missing
link between statistical and locality (commensurability) properties of the
observables of spacelike separated observers in relativistic quantum physics,
envisaged four decades ago by Haag and Kastler. It is based on a discussion of
coincidence experiments and suggests a physically meaningful quantitative
measure of possible violations of Einstein causality.Comment: 3 pages, no figure
Transplantation of Local Nets and Geometric Modular Action on Robertson-Walker Space-Times
A novel method of transplanting algebras of observables from de Sitter space
to a large class of Robertson-Walker space-times is exhibited. It allows one to
establish the existence of an abundance of local nets on these spaces which
comply with a recently proposed condition of geometric modular action. The
corresponding modular symmetry groups appearing in these examples also satisfy
a condition of modular stability, which has been suggested as a substitute for
the requirement of positivity of the energy in Minkowski space. Moreover, they
exemplify the conjecture that the modular symmetry groups are generically
larger than the isometry and conformal groups of the underlying space-times.Comment: 20 pages, 1 figure, v2: minor changes in the wordin
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