6,908 research outputs found
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
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
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
Passive States for Essential Observers
The aim of this note is to present a unified approach to the results given in
\cite{bb99} and \cite{bs04} which also covers examples of models not presented
in these two papers (e.g. -dimensional Minkowski space-time for ).
Assuming that a state is passive for an observer travelling along certain
(essential) worldlines, we show that this state is invariant under the isometry
group, is a KMS-state for the observer at a temperature uniquely determined by
the structure constants of the Lie algebra involved and fulfills (a variant of)
the Reeh-Schlieder property. Also the modular objects associated to such a
state and the observable algebra of an observer are computed and a version of
weak locality is examined.Comment: 27 page
Constant Savings Rates and Quasi-Arithmetic Population Growth under Exhaustible Resource Constraints
In the Dasgupta-Heal-Solow-Stiglitz model of capital accumulation and resource depletion we show the following equivalence: If an efficient path has constant (gross and net of population growth) savings rates, then population growth must be quasi-arithmetic and the path is a maximin or a classical utilitarian optimum. Conversely, if a path is optimal according to maximin or classical utilitarianism (with constant elasticity of marginal utility) under quasiarithmetic population growth, then the (gross and net of population growth) savings rates converge asymptotically to constants.constant savings rate, quasi-arithmetic population growth
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
Asymptotic completeness in a class of massless relativistic quantum field theories
This paper presents the first examples of massless relativistic quantum field
theories which are interacting and asymptotically complete. These
two-dimensional theories are obtained by an application of a deformation
procedure, introduced recently by Grosse and Lechner, to chiral conformal
quantum field theories. The resulting models may not be strictly local, but
they contain observables localized in spacelike wedges. It is shown that the
scattering theory for waves in two dimensions, due to Buchholz, is still valid
under these weaker assumptions. The concepts of interaction and asymptotic
completeness, provided by this theory, are adopted in the present
investigation.Comment: 15 pages, LaTeX. As appeared in Communications in Mathematical
Physic
Spin, Statistics, and Reflections, II. Lorentz Invariance
The analysis of the relation between modular PCT-symmetry -- a
consequence of the Unruh effect -- and Pauli's spin-statistics relation is
continued. The result in the predecessor to this article is extended to the
Lorentz symmetric situation. A model \G_L of the universal covering
\widetilde{L_+^\uparrow}\cong SL(2,\complex) of the restricted Lorentz group
is modelled as a reflection group at the classical level. Based
on this picture, a representation of \G_L is constructed from pairs of
modular PCT-conjugations, and this representation can easily be verified to
satisfy the spin-statistics relation
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