7,954 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
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
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
String-- and Brane--Localized Causal Fields in a Strongly Nonlocal Model
We study a weakly local, but nonlocal model in spacetime dimension
and prove that it is maximally nonlocal in a certain specific quantitative
sense. Nevertheless, depending on the number of dimensions , it has
string--localized or brane--localized operators which commute at spatial
distances. In two spacetime dimensions, the model even comprises a covariant
and local subnet of operators localized in bounded subsets of Minkowski space
which has a nontrivial scattering matrix. The model thus exemplifies the
algebraic construction of local observables from algebras associated with
nonlocal fields.Comment: paper re-written with a change of emphasis and new result
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
Existence and Warr Neutrality for Matching Equilibria in a Public Good Economy: An Aggregative Game Approach
Using the aggregative game approach as developed by Cornes and Hartley (2003, 2007) this paper analyzes the conditions under which matching mechanisms in a public good economy lead to interior matching equilibria in which all agents make strictly positive flat contributions to the public good. In particular we show that the distribution of income among the agents is a crucial determinant for the existence of interior matching equilibria. In addition, we explore which matching mechanisms show Warr neutrality and how the size of the economy affects the possibility of implementing a certain type of Pareto optimal solutions through matching.
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
Kinetic-Energy Density-Functional Theory on a Lattice
We present a kinetic-energy density-functional theory and the corresponding
kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that by including
more observables explicitly in a density-functional approach already simple
approximation strategies lead to very accurate results. Here we promote the
kinetic-energy density to a fundamental variable along side the density and
show for specific cases (analytically and numerically) that there is a
one-to-one correspondence between the external pair of on-site potential and
site-dependent hopping and the internal pair of density and kinetic-energy
density. Based on this mapping we establish two unknown effective fields, the
mean-field exchange-correlation potential and the mean-field
exchange-correlation hopping, that force the keKS system to generate the same
kinetic-energy density and density as the fully interacting one. We show, by a
decomposition based on the equations of motions for the density and the
kinetic-energy density, that we can construct simple orbital-dependent
functionals that outperform the corresponding exact-exchange Kohn-Sham (KS)
approximation of standard density-functional theory. We do so by considering
the exact KS and keKS systems and compare the unknown correlation contributions
as well as by comparing self-consistent calculations based on the mean-field
exchange for the keKS and the exact-exchange for the KS system, respectively
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