Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map

We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.     

Passivity and Microlocal Spectrum Condition

In the setting of vector-valued quantum fields obeying a linear wave-equation in a globally hyperbolic, stationary spacetime, it is shown that the two-point functions of passive quantum states (mixtures of ground- or KMS-states) fulfill the microlocal spectrum condition (which in the case of the canonically quantized scalar field is equivalent to saying that the two-pnt function is of Hadamard form). The fields can be of bosonic or fermionic character. We also give an abstract version of this result by showing that passive states of a topological *-dynamical system have an asymptotic pair correlation spectrum of a specific type. Received: 9 February 2000 / Accepted: 7 June 2000     

Synthesis of a polystyrene-arm-polybutadiene-arm-poly(methyl methacrylate) triarm star copolymer

The straightforward synthesis of a polystyrene-arm-polybutadiene-arm-poly(methyl methacrylate) triarm star copolymer has been successfully realized by a sequence of reactions which involves the sequential addition of a living polybutadienyllithium to a polystyrene macromonomer with a terminal 1,1-diphenylethylene unit and subsequent polymerization of methyl methacrylate. The high-molecular-weight polystyrene-arm-polybutadiene-arm-poly(methyl methacrylate) star copolymer shows microphase separation into three phases.     

VUV emission of Xe III levels excited by electron impact viaN 4,5 00 Auger transitions

Optical excitation functions were measured for Xenon emission lines. The Xe III 5s 5p ⁵ levels are excited in two different processes, by a direct two electron ejection and by a 4d ionization followed by an Auger decay. An emission line found at 1089.0 Å is excited by 4d ionization. This line is assigned to the Xe III transition 5s5p ^{5 1} P ⁰ —5s ⁰ 5p ^{6 1} S. The¹ S energy level amounts to 26.14 eV.     

Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras

Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic kinematical observables and represents it through operators on a suitable Hilbert space. In a second step, one implements the constraints. The main result of the paper concerns the representation theory of the kinematical algebra: We show that there is only one cyclic representation invariant under spatial diffeomorphisms.While this result is particularly important for loop quantum gravity, we are rather general: The precise definition of the abstract *-algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group. The variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection. The uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory.     

Iterative Denoising

One problem in many fields is knowledge discovery in heterogeneous, high-dimensional data. As an example, in text mining an analyst often wishes to identify meaningful, implicit, and previously unknown information in an unstructured corpus. Lack of metadata and the complexities of document space make this task difficult. We describe Iterative Denoising, a methodology for knowledge discovery in large heterogeneous datasets that allows a user to visualize and to discover potentially meaningful relationships and structures. In addition, we demonstrate the features of this methodology in the analysis of a heterogeneous Science News corpus.     

Electrodynamics of Perfect Conductors

The most general electrodynamic equations of a perfect conducting state are obtained using a variational principle in a classical framework, following an approach by Pierre-Gilles de Gennes. London equations are derived as the time-independent case of these equations, corresponding to the magnetostatic minimal energy state of the perfect conducting system. For further confirmation, the same equations are also derived in the classical limit of the Coleman-Weinberg model, the most successful quantum macroscopic theory of superconductivity. The magnetic field expulsion is, therefore, a direct consequence of zero resistivity and not an exclusive property of superconductors.