Observables and Statistical Maps

This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events) and the set of probability measures on a measurable space . An observable is defined, where is the value space of X. It is noted that there exists a one-to-one correspondence between states on and elements of and between observables and -morphisms from to . Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived.     

Glueball Spectroscopy in Regge Phenomenology

We show that linear Regge trajectories for mesons and glueballs, and the cubic mass spectrum associated with them, determine a relation between the masses of the meson and the scalar glueball, , which implies MeV. We also discuss relations between the masses of the scalar, tensor and 3^-- glueballs, , which imply MeV.     

On Continuous and Differential Hochschild Cohomology

We show that there are canonical isomorphisms between Hochschild cohomology spaces , where is the algebra of smooth functions on a manifold M and the space of skew multivector fields over M. This implies that continuous and differential deformation theories of coincide.     

Multipoint Series of Gromov–Witten Invariants of CP1

We derive explicit formulas for the multipoint series of in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of . We also obtain explicit formulas for the Hodge integrals , in the cases i=0 and 1.     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

On the Product of Real Spectral Triples

The product of two real spectral triples and , the first of which is necessarily even, was defined by A.Connes as given by and, in the even-even case, by . Generically it is assumed that the real structure obeys the relations , , , where the -sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes' >-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this -sign table. In this Letter, we propose an alternative definition of the product real structure such that the -sign table is also satisfied by the product.     

A Generator for the Weert Superpotential

Weert found a superpotential for the bounded part of the Maxwelltensor associatedto the Lienard–Wiechert field. Here we obtain afourth-rank generator for the superpotential .     

Energy dependence of the charge exchange reaction from muonic hydrogen to oxygen

The charge exchange reaction of negative muons from the atom to oxygen has been measured in gaseous mixtures of H₂ + O₂. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of , describing the transfer from the ground state of thermalized atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate =3.9 10¹¹ s^-1 in the energy interval 0.12–0.22 eV. The analysis with the model of Two components shows that all measured time spectra can be reproduced with the same set of parameters.     

Thermoelectric power of YBa2Cu3Ox in equilibrium with gas phases

Thermoelectric power (TP) and electrical conductivity (EC) measurements were performed for YEa₂Cu₃O_x at 1128 K under controlled oxygen partial pressure varying between 50 and 10⁵ Pa. Three regimes are observed for the electrical properties. At low both TP and EC remain constant with . In the medium range sharp changes of both electrical parameters occur; TP changes sign from positive above 4×10² Pa to negative below this value. In the high region (>7.6×10³ Pa) TP vs log exhibits two slopes; 5.1 below 1.5×10⁴ Pa and 8.4 above this value. The slopes can be discussed in terms of the defect structure involving singly and doubly ionized oxygen vacancies below and above 7.6×10³ Pa, respectively.     

Preferred Invariant Symplectic Connections on Compact Coadjoint Orbits

Let be the Haag--Kastler net generated by the (2) chiral current algebra at level 1. We classify the SL(2, )-covariant subsystems by showing that they are all fixed points nets ^H for some subgroup H of the gauge automorphisms group SO(3) of . Then, using the fact that the net ₁ generated by the (1) chiral current can be regarded as a subsystem of , we classify the subsystems of ₁. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem .     

Covariant (hh′)-Deformed Bosonic and Fermionic Algebras as Contraction Limits of q-Deformed Ones

GL_h(n) ×GL_h(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras are built in terms of thecorresponding R_h and -matrices by contracting theGL_q(n) × -covariant q-bosonic (or q-fermionic) algebras , = 1, 2.When using a basis of wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra U_q(gl(n)) , a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingU_h(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some U_h(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of (2, 1).     

Poincaré-Invariant Markov Processes and Gaussian Random Fields on Relativistic Phase Space

We give a complete characterization, including a Lévy–Itô decomposition, of Poincaré-invariant Markov processes on , the relativistic phase space in 1+1 spacetime dimensions. Then, by means of such processes, we construct Poincaré-invariant Gaussian random fields, and we prove a no-go theorem for the random fields corresponding to Brownian motions on .     

Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with Finite-Density Initial Data. II. Dark Solitons on Continua

For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation ( NLSE), , with finite-density initial data

Exactly Solvable su(N) Mixed Spin Ladders

It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin- spin-1 ladder, a mixed spin- spin- ladder and a spin-1 ladder with biquadratic interactions.     

SU(1, 1) Perturbations of the s-Wave Morse Potential Problem

A purely algebraic perturbation theory based on deforming the generators of the dynamical group SU(1, 1) is applied to the l = 0 Morse potential problem with . In particular, perturbations of the form and are treated explicitly.     

Poisson Structures for Dispersionless Integrable Systems and Associated W-Algebras

In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators . The reduction of the Poisson structure to the symplectic submanifold gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as , where means the multiplicity of roots and to the case (b) is defined by where is the multiplicity of poles. We prove that -algebra is isomorphic via a transformation to U(1) with m= . We also give the explicit free fields representations for these W-algebras.     

Integrals of Vertex Operators and uantum Shuffles

Given a braided vector space , we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on . Using the quantum shuffle construction of the 'upper triangular part' of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of .     

Hyperbolic Conformal Geometry with Clifford Algebra

In this paper, we study hyperbolic conformal geometry following a Clifford algebraic approach. Similar to embedding an affine space into a one-dimensional higher linear space, we embed the hyperboloid model of the hyperbolic n-space in into . The model is convenient for the study of hyperbolic conformal properties. Besides investigating various properties of the model, we also study conformal transformations using their versor representations.