Unbounded derivations commuting with compact group actions

Let be a closed * derivation in aC* algebra which commutes with an ergodic action of a compact group on . Then generates aC* dynamics of . Similar results are obtained for non-ergodic actions on abelianC* algebras and on the algebra of compact operators.Research supported by N.S.F.     

Slepton and squark production and decay inep collisions at the LHC

We present a detailed study of and and the subsequent decays of , , and at the LHC . We explore the relevant supersymmetry parameter range. We calculate the cross sections as well as the rates for interesting signatures such as the production of one or two leptons on the lepton side.     

SU q (2) covariant\hat R-matrices for reducible representations

We consider SU _q (2) covariant -matrices for the reducible3 1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known -matrices for SO _q (3) and SO _q (3, 1). Also, they are the three -matrices which can be constructed by using four different SU _q (2) doublets. Only two of the three -matrices allow a differential structure on the reducible four-dimensional quantum space.     

Logarithmic Sobolev inequality for lattice gases with mixing conditions

Let denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let be the corresponding canonical measure defined by conditioning on . Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed, is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for forall chemical potentials . We prove that for any probability densityf with respect to ; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship.     

Derivations and automorphisms of operator algebras

The theorem that each derivation of aC*-algebra extends to an inner derivation of the weak-operator closure ( )^– of in each faithful representation of is proved in sketch and used to study the automorphism group of in its norm topology. It is proved that the connected component of the identity in this group contains the open ball of radius 2 with centerl and that each automorphism in extends to an inner automorphism of ( )^–.Research conducted with the partial support of the NSF and ONR.     

On the support of the Ashtekar-Lewandowski measure

We show that the Ashtekar-Isham extension of the configuration space of Yang-Mills theories is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that is contained in a zero measure subset of with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on . Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the extended configuration space .     

Central decomposition of invariant states applications to the groups of time translations and of euclidean transformations in algebraic field theory

With aC*-algebra with unit andgG _g a homomorphic map of a groupG into the automorphism group ofG, the central measure of a state of is invariant under the action ofG (in the state space of ) iff is -invariant. Furthermore if the pair { ,G} is asymptotically abelian, is ergodic iff is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on , the associated covariant representations of { , } are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states.     

Global conformal invariance in quantum field theory

Suppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal groupSO _e (5,1). We show that its Hilbert space of physical states carries then a unitary representation of the universal (-sheeted) covering group* of the Minkowskian conformal group SO _e (4, 2)₂. The Wightman functions can be analytically continued to a domain of holomorphy which has as a real boundary an -sheeted covering of Minkowski-spaceM ⁴. It is known that* can act on this space and that admits a globally*-invariant causal ordering; is thus the natural space on which a globally*-invariant local QFT could live. We discuss some of the properties of such a theory, in particular the spectrum of the conformal HamiltonianH=1/2(P ⁰+K ⁰).As a tool we use a generalized Hille-Yosida theorem for Lie semigroups. Such a theorem is stated and proven in Appendix C. It enables us to analytically continue contractive representations of a certain maximal subsemigroup of to unitary representations of*.     

Quantum principal commutative subalgebra in the nilpotent part ofU_q \widehat{sl}_2 and lattice KdV variables

We propose a quantum lattice version of B. Feigin and E. Frenkel's constructions, identifying the KdV differential polynomials with functions on a homogeneous space under the nilpotent part of . We construct an action of the nilpotent part of on their lattice counterparts, and embed the lattice variables in a , coinduced from a quantum version of the principal commutative subalgebra, which is defined using the identification of with its dual algebra.     

Ensemble and trajectory statistics in a nonlinear partial differential equation

We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean and variance are well-characterized functions of the noise statistics, and and depend on . When noise is continuously present along the trajectory, and are independent of the noise statistics and . However, in their evolution toward and , both _u (t, x) and _u ² (t, x) depend on the noise and.     

Four-quark states and nucleon-antinucleon annihilation within the quark model with QCD vacuum-induced interaction

The spectrum of , J^p=0⁺, 2⁺ mesons is discussed. We have shown that due to instanton-induced forces the physical states are strong mixtures of theSU _f (3) group basis states. The cross-sections for annihilation of the system into mesons are obtained. Thea ₀(980) meson is considered as meson consisting of 9 _f and 36 _f plets. The branchings are also predicted for the cross-sections for production of thea ₀(980) and tensor mesons in annihilation.     

Instabilities of certain empty Robertson-Walker space-times

Results are established concerning perturbations of each empty Robertson-Walker space-time (M, g) with a nonvanishing cosmological constant. The perturbed space-times have the general form ( ) with an extension ofM, and lying in an open neighborhood of g in a type ofW ^m topology. These results indicate that large classes of such perturbations give rise to space-times which suffer from one of two types of incompleteness.     

Comments on “power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas”

A simple argument is presented by which one can show that the critical inverse temperature _c of a two-dimensional Coulomb gas (standard or hard-core) with activityz satisfies , where in the low-activity limit. Previous results yield .     

On the purification of factor states

Let be aC*-algebra and be an opposite algebra. Notions of exact andj-positive states of are introduced. It is shown, that any factor state of can be extended to a pure exactj-positive state of . The correspondence generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states ₁ and ₂ are quasi-equivalent if and only if their purifications and are equivalent.     

Recursion method for the density of states and spectral dimension of percolation networks

We use the recursion method to calculate the vibrational density of states of site percolation clusters slightly above the percolation threshold. It is found that is proportional to at long wavelengths. At shorter length scales, is proportional to , with the fraction dimension . The cross-over from phonon to fraction regime is characterized by a rapid rise in in agreement with effective medium calculations.     

Limiting behavior of asymptotically flat gravitational fields

Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x ^A ) , wherex ^A (A = 2, 3) are angular coordinates, they show that , where ₁ 2 and ₁<₀; , where ₂ 1 and ₁< ₁; and ₄ and ₃ peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x ^A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.     

Entropy functionals of Kolmogorov-Sinai type and their limit theorems

Two functionals and are introduced forC ^*-dynamical systems with invariant states and stationary channels. It is shown that the Kolmogorov-Sinai-type theorems hold for these functionals and . Our functionals and are set within the framework of quantum information theory and generalize a quantum KS entropy by CNT and the mutual entropy by Ohya.     

Bethe subalgebras in twisted Yangians

We study analogues of the Yangian of the Lie algebra for the other classical Lie algebras and . We call them twisted Yangians. They are coideal subalgebras in the Yangian of and admit homomorphisms onto the universal enveloping algebras U( ) and U( ) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in U( ) and U( ) of these subalgebras are also maximal commutative.     

Scaling characteristics of ac conductivity and dielectric function in fractal regime of the metal-insulator transition

An analysis of the ac conductivity _ac(), and the ac dielectric constant, (), of the metal-insulator percolation systems is presented in the critical regime near the transition threshold. It is argued that the polarization and relaxation of the finite fractal metallic clusters play dominant roles in controlling the dynamic response of the system on both sides of the threshold. The relaxation time constant of a fractal cluster is shown to scale with its size as withd _t = 4 – 2d +d _c + /, whered is tge Euclidean dimension, andd _c , , and are the scaling indices for the charging, the dc conductivity, and the correlation length respectively. The average time dependent response of the system is shown to scale with a new time scale , where is the correlation length and ₀ is a microscopic time constant. It is shown that at frequencies and with /d_t 1, in close agreement with experiments. The effects of the anomalous transport along the infinite cluster and the medium polarizability are also discussed.     

Evidence for non-q \bar q mesons

The non-Abelian nature of QCD suggests that particles that have a gluon constituent, such as glueballs or hybrids, should exist. In addition,q q states are also predicted. This paper describes a search for these non-q q mesons performed by experiment WA 76 using the CERN Omega Spectrometer and discusses three candidates which have been observed.Invited talk at HEXAM 89, Bechyn Castle, Czechoslovakia, June 25–30, 1989.