Editorial

The production of charmed mesons ,D ^± , andD ^*± is studied in a sample of 478,000 hadronicZ decays. The production rates are measured to be

Bounded speed of propagation for solutions to radiative transfer equations

The Radiative Transfer Equation is the nonlinear transport equation

Conformally Invariant Quantization at Order Three

Let (M, g) be a pseudo-Riemannian manifold and the space of densities of degree on M. Denote the space of differential operators from to of order k and S _k with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map . This result generalizes that of Duval and Ovsienko.     

From quantum to elliptic algebras

It is shown that the elliptic algebra at the critical level c = –2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p ^m = q ^c+2 for , they commute when in addition p = q ^2k for k integer non-zero, and they belong to the center of when k is odd. The Poisson structures obtained for t(z) in these classical limits contain the q-deformed Virasoro algebra, characterizing the structures at p q ^2k as new algebras.     

Isospectral Hamiltonian flows in finite and infinite dimensions

The approach to isospectral Hamiltonian flow introduced in part I is further developed to include integration of flows with singular spectral curves. The flow on finite dimensional Ad^*-invariant Poisson submanifolds of the dual of the positive part of the loop algebra is obtained through a generalization of the standard method of linearization on the Jacobi variety of the invariant spectral curveS. These curves are embedded in the total space of a line bundleTP ₁(C), allowing an explicit analysis of singularities arising from the structure of the image of a moment map from the space of rank-r deformations of a fixedN×N matrixA. It is shown how the linear flow of line bundles over a suitably desingularized curve may be used to determine both the flow of matricial polynomialsL() and the Hamiltonian flow in the spaceM _N,r×M_N,r in terms of -functions. The resulting flows are proved to be completely integrable. The reductions to subalgebras developed in part I are shown to correspond to invariance of the spectral curves and line bundles under certain linear or anti-linear involutions. The integration of two examples from part I is given to illustrate the method: the Rosochatius system, and the CNLS (coupled non-linear Schrödinger) equation.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and by U.S. Army grant DAA L03-87-K-0110     

Superconformal current algebras and their unitary representations

A natural supersymmetric extension is defined of the current (= affine Kac-Moody Lie) algebra ; it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory (QFT), and hence appears as an ingredient in superstring models. All unitary irreducible positive energy representations of are constructed. They extend to unitary representations of the semidirect sumS (G) of with the superconformal algebra of Neveu-Schwarz, for , or of Ramond, for =0.On leave of absence from the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences, BG-1184 Sofia, Bulgaria     

The droplet in the tube: A case of phase transition in the canonical ensemble

We consider the 2-dimensional Ising model with ferromagnetic nearest neighbour interaction at inverse temperature. LetS _N = _t be the total magnetization inside anN×N square box, ^per be the Gibbs state in with periodic b.c., andm() be the spontaneous magnetization. We show the existence of the limit

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Bound States in a Locally Deformed Waveguide: The Critical Case

We consider the Dirichlet Laplacian for astrip in with one straight boundary and a width , where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase, , the operator has nobound statesfor small .On the otherhand, a weakly bound state existsprovided . In thatcase, there are positive c ₁,c ₂ suchthat the corresponding eigenvalue satisfies for all sufficiently small.     

A mathematical condition for a sublattice of a propositional system to represent a physical subsystem,with a physical interpretation

We display three equivalent conditions for a sublattice, isomorphic to aP , of the propositional systemP() of a quantum system to be the representation of a physical subsystem (see [1]). These conditions are valid for dim 3. We prove that one of them is still necessary and sufficient if dim <3. A physical interpretation of this condition is given.Wetenschappelijke medewerkers bij het Interuniversitair Instituut voor Kernwetenschappen (in het kader van navorsingsprogramma 21 EN).     

CP-violating effects inZ decays to τ leptons

We calculate CP-odd correlations inZ decays to leptons, . These correlations are sensitive to the weak dipole moment of the . With 10⁷ producedZ particles and with observation of the decay channels and v we estimate that can be determined with an accuracy of about (1 s.d.).     

A measurement of the forward-backward asymmetry of e+e?→bb by applying a jet charge algorithm to lifetime tagged events

The forward-backward asymmetry of has been measured using approximately 2.15 million hadronicZ ⁰ decays collected at the LEP e⁺e^– collider with the OPAL detector. A lifetime tag technique was used to select an enriched event sample. The measurement of the asymmetry was then performed using a jet charge algorithm to determine the direction of the primary quark. Values of:

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.     

On the positivity of the effective action in a theory of random surfaces

It is shown that the functional , defined onC functions on the two-dimensional sphere, satisfies the inequalityS[]0 if is subject to the constraint . The minimumS[]=0 is attained at the solutions of the Euler-Lagrange equations. The proof is based on a sharper version of Moser-Trudinger's inequality (due to Aubin) which holds under the additional constraint ; this condition can always be satisfied by exploiting the invariance ofS[] under the conformal transformations ofS ². The result is relevant for a recently proposed formulation of a theory of random surfaces.On leave from: Istituto di Fisica dell'Università di Parma, Sezione di Fisica Teorica, Parma, Italy     

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.     

Associated production of a light Higgs boson and a chargino pair in the MSSM at linear colliders

In the minimal supersymmetric standard model (MSSM), we study the light Higgs boson radiation off a light-chargino pair in the process at linear colliders with GeV. We analyze cross sections in the regions of the MSSM parameter space where the process cannot proceed via on-shell production and subsequent decay of either heavier charginos or the pseudoscalar Higgs boson A. Cross sections up to a few fb are allowed, according to present experimental limits on the Higgs boson, chargino and sneutrino masses. We also show how a measurement of the production rate could provide a determination of the Higgs boson couplings to charginos.Received: 24 June 2004, Revised: 13 May 2005, Published online: 19 July 2005     

BV Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of(W) Strings

Given a simple, simply laced, complex Lie algebra corresponding to the Lie group G, let be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra whose underlying graded commutative algebra is given by the cohomology, with respect to , of the algebra of regular functions on G with values in . We conjecture that describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical string. The conjecture is verified in the two explicitly known cases, ₂ (the Virasoro string) and ₃ (the string).     

On equivalent-neighbour,random site models of disordered systems

Models of random systems whose Hamiltonian reads , where and _i ,=1,...,n are independent, identically distributed random variables are discussed.J _ij are assumed to be symmetric, with respect toJ ₀, random variables and also symmetric functions of components of . A question of dependence of a phase diagram on a probability distribution of is addressed. A class of distributions and interactionsJ _ij , which give rise to phase diagrams called typical is selected. Then a problem of obtaining typical phase diagrams, containing a certain region with an infinite number of pure phases, is studied.     

Conformal Quantum Effects and the Anisotropic Singularities of Scalar-Tensor Theories of Gravity

We show that the inclusion of a term C _abcd C ^abcd in the action can remove the recently described anisotropic singularity occurring on the hypersurface F () = 0 of scalar-tensor theories of gravity of the type