43 research outputs found
Geometric Modular Action, Wedge Duality and Lorentz Covariance are Equivalent for Generalized Free Fields
The Tomita-Takesaki modular groups and conjugations for the observable
algebras of space-like wedges and the vacuum state are computed for
translationally covariant, but possibly not Lorentz covariant, generalized free
quantum fields in arbitrary space-time dimension d. It is shown that for the condition of geometric modular action (CGMA) of Buchholz, Dreyer, Florig
and Summers \cite{BDFS}, Lorentz covariance and wedge duality are all
equivalent in these models. The same holds for d=3 if there is a mass gap. For
massless fields in d=3, and for d=2 and arbitrary mass, CGMA does not imply
Lorentz covariance of the field itself, but only of the maximal local net
generated by the field
Characterizing the Load Deformation Behaviour of Steel Deck Diaphragms
Lateral loads flow through a building’s horizontal roof and floor diaphragms before being transferred to the vertical lateral force resisting system (e.g. braced frames, moment frames or shear walls). These diaphragms are therefore a critical structural component in the resistance of lateral loads. A review of the literature shows that a large number of experimental programs have been performed to obtain the in-plane load-deformation behavior of steel deck and concrete on steel deck diaphragms. The tested diaphragm behavior was found to be dependent on a set of factors including loading protocol, fastener type, fastener size and spacing, and more. There does not currently exist a single, unifying review of these diaphragm tests and their relevant results. A research program is being conducted to collect and consolidate the available literature about tested steel deck diaphragms and their results. A database has been created that includes over 450 tested specimens with more than 130 cyclic tests. In addition, an effort is made to characterize diaphragms’ load-deformation response as grouped by sidelap and support fastener type. The test programs and results collected into this database as well as the characterization of diaphragm behavior are discussed in this paper
Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory
Einstein introduced the locality principle which states that all physical
effect in some finite space-time region does not influence its space-like
separated finite region. Recently, in algebraic quantum field theory, R\'{e}dei
captured the idea of the locality principle by the notion of operational
separability. The operation in operational separability is performed in some
finite space-time region, and leaves unchanged the state in its space-like
separated finite space-time region. This operation is defined with a completely
positive map. In the present paper, we justify using a completely positive map
as a local operation in algebraic quantum field theory, and show that this
local operation can be approximately written with Kraus operators under the
funnel property
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
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
Remarks on Causality in Relativistic Quantum Field Theory
It is shown that the correlations predicted by relativistic quantum field
theory in locally normal states between projections in local von Neumann
algebras \cA(V_1),\cA(V_2) associated with spacelike separated spacetime
regions have a (Reichenbachian) common cause located in the union of
the backward light cones of and . Further comments on causality and
independence in quantum field theory are made.Comment: 10 pages, Latex, Quantum Structures 2002 Conference Proceedings
submission. Minor revision of the order of definitions on p.
Infraparticles with superselected direction of motion in two-dimensional conformal field theory
Particle aspects of two-dimensional conformal field theories are
investigated, using methods from algebraic quantum field theory. The results
include asymptotic completeness in terms of (counterparts of) Wigner particles
in any vacuum representation and the existence of (counterparts of)
infraparticles in any charged irreducible product representation of a given
chiral conformal field theory. Moreover, an interesting interplay between the
infraparticle's direction of motion and the superselection structure is
demonstrated in a large class of examples. This phenomenon resembles the
electron's momentum superselection expected in quantum electrodynamics.Comment: 34 pages, no figure. The final version is available under Open
Access. CC-B
Core Equivalence for Hierarchic Equilibria.
The standard equivalence result on core and Walras equilibrium allocations uses a non-satiation and an interiority assumption. Konovalov introduced the rejective core for exchange economies with possibly satiated preferences and proved that there, the fuzzy rejective core coincides with the set of dividend equilibria provided an interiority assumption holds.MATHEMATICAL ANALYSIS ; ECONOMICS ; DIVIDENDS
Computational Aspects of Linear Exchange Economies.
The set of equilibrium prices in linear exchange economies is by Mertens (1996) a convex polyhedral cone (after adding {0}). We give a constructive proof of this fact. From this, we derive a lower semi-continuity property of the equilibrium price correspondence. The set of equilibrium allocations is a closed, convex polyhedron (Bonnisseau, Florig and Jofré 1997b). We give a characterization of this set which allows to compute it.PRICES ; ECONOMIC EQUILIBRIUM ; UTILITY FUNCTIONS