7,222 research outputs found
Optimal purifications and fidelity for displaced thermal states
We evaluate the Uhlmann fidelity between two one-mode displaced thermal
states as the maximal probability transition between appropriate purifications
of the given states. The optimal purifications defining the fidelity are proved
to be two-mode displaced Gaussian states.Comment: published versio
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
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
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
The unmasking of thermal Goldstone bosons
The problem of extracting the modes of Goldstone bosons from a thermal
background is reconsidered in the framework of relativistic quantum field
theory. It is shown that in the case of spontaneous breakdown of an internal
bosonic symmetry a recently established decomposition of thermal correlation
functions contains certain specific contributions which can be attributed to a
particle of zero mass.Comment: 7 pages, LaTeX; new and considerably strengthened results after Eq.
(14); to appear in Phys. Rev.
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
New Concepts in Particle Physics from Solution of an Old Problem
Recent ideas on modular localization in local quantum physics are used to
clarify the relation between on- and off-shell quantities in particle physics;
in particular the relation between on-shell crossing symmetry and off-shell
Einstein causality. Among the collateral results of this new nonperturbative
approach are profound relations between crossing symmetry of particle physics
and Hawking-Unruh like thermal aspects (KMS property, entropy attached to
horizons) of quantum matter behind causal horizons, aspects which hitherto were
exclusively related with Killing horizons in curved spacetime rather than with
localization aspects in Minkowski space particle physics. The scope of this
modular framework is amazingly wide and ranges from providing a conceptual
basis for the d=1+1 bootstrap-formfactor program for factorizable d=1+1 models
to a decomposition theory of QFT's in terms of a finite collection of unitarily
equivalent chiral conformal theories placed a specified relative position
within a common Hilbert space (in d=1+1 a holographic relation and in higher
dimensions more like a scanning). The new framework gives a spacetime
interpretation to the Zamolodchikov-Faddeev algebra and explains its thermal
aspects.Comment: In this form it will appear in JPA Math Gen, 47 pages tcilate
Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime
We derive for a pair of operators on a symplectic space which are adjoints of
each other with respect to the symplectic form (that is, they are sympletically
adjoint) that, if they are bounded for some scalar product on the symplectic
space dominating the symplectic form, then they are bounded with respect to a
one-parametric family of scalar products canonically associated with the
initially given one, among them being its ``purification''. As a typical
example we consider a scalar field on a globally hyperbolic spacetime governed
by the Klein-Gordon equation; the classical system is described by a symplectic
space and the temporal evolution by symplectomorphisms (which are
symplectically adjoint to their inverses). A natural scalar product is that
inducing the classical energy norm, and an application of the above result
yields that its ``purification'' induces on the one-particle space of the
quantized system a topology which coincides with that given by the two-point
functions of quasifree Hadamard states. These findings will be shown to lead to
new results concerning the structure of the local (von Neumann)
observable-algebras in representations of quasifree Hadamard states of the
Klein-Gordon field in an arbitrary globally hyperbolic spacetime, such as local
definiteness, local primarity and Haag-duality (and also split- and type
III_1-properties). A brief review of this circle of notions, as well as of
properties of Hadamard states, forms part of the article.Comment: 42 pages, LaTeX. The Def. 3.3 was incomplete and this has been
corrected. Several misprints have been removed. All results and proofs remain
unchange
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