8,257 research outputs found
A sharpened nuclearity condition for massless fields
A recently proposed phase space condition which comprises information about
the vacuum structure and timelike asymptotic behavior of physical states is
verified in massless free field theory. There follow interesting conclusions
about the momentum transfer of local operators in this model.Comment: 13 pages, LaTeX. As appeared in Letters in Mathematical Physic
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
Nuclearity and Thermal States in Conformal Field Theory
We introduce a new type of spectral density condition, that we call
L^2-nuclearity. One formulation concerns lowest weight unitary representations
of SL(2,R) and turns out to be equivalent to the existence of characters. A
second formulation concerns inclusions of local observable von Neumann algebras
in Quantum Field Theory. We show the two formulations to agree in chiral
Conformal QFT and, starting from the trace class condition for the semigroup
generated by the conformal Hamiltonian L_0, we infer and naturally estimate the
Buchholz-Wichmann nuclearity condition and the (distal) split property. As a
corollary, if L_0 is log-elliptic, the Buchholz-Junglas set up is realized and
so there exists a beta-KMS state for the translation dynamics on the net of
C*-algebras for every inverse temperature beta>0. We include further
discussions on higher dimensional spacetimes. In particular, we verify that
L^2-nuclearity is satisfied for the scalar, massless Klein-Gordon field.Comment: 37 pages, minor correction
Geometric modular action for disjoint intervals and boundary conformal field theory
In suitable states, the modular group of local algebras associated with
unions of disjoint intervals in chiral conformal quantum field theory acts
geometrically. We translate this result into the setting of boundary conformal
QFT and interpret it as a relation between temperature and acceleration. We
also discuss aspects ("mixing" and "charge splitting") of geometric modular
action for unions of disjoint intervals in the vacuum state.Comment: Dedicated to John E. Roberts on the occasion of his 70th birthday; 24
pages, 3 figure
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
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
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
Deformations of Fermionic Quantum Field Theories and Integrable Models
Considering the model of a scalar massive Fermion, it is shown that by means
of deformation techniques it is possible to obtain all integrable quantum field
theoretic models on two-dimensional Minkowski space which have factorizing
S-matrices corresponding to two-particle scattering functions S_2 satisfying
S_2(0) = -1. Among these models there is for example the Sinh-Gordon model. Our
analysis provides a complement to recent developments regarding deformations of
quantum field theories. The deformed model is investigated also in higher
dimensions. In particular, locality and covariance properties are analyzed.Comment: 20 page
The Hot Bang state of massless fermions
In 2002, a method has been proposed by Buchholz et al. in the context of
Local Quantum Physics, to characterize states that are locally in thermodynamic
equilibrium. It could be shown for the model of massless bosons that these
states exhibit quite interesting properties. The mean phase-space density
satisfies a transport equation, and many of these states break time reversal
symmetry. Moreover, an explicit example of such a state, called the Hot Bang
state, could be found, which models the future of a temperature singularity.
However, although the general results carry over to the fermionic case easily,
the proof of existence of an analogue of the Hot Bang state is not quite that
straightforward. The proof will be given in this paper. Moreover, we will
discuss some of the mathematical subtleties which arise in the fermionic case.Comment: 17 page
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