Combinatorial quantisation of Euclidean gravity in three dimensions

In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson structure of the moduli space is given explicitly in terms of a classical r-matrix. It is shown that the quantum R-matrix of the quantum double D(SU(2)) provides a quantisation of that Poisson structure.Comment: cosmetic chang

Quantum gravity and non-commutative spacetimes in three dimensions: a unified approach

These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants (c,G,\Lambda,\hbar) enter as deformation parameters. The classical situation is summarised, where solutions can be characterised in terms of model spacetimes (which depend on c and \Lambda), together with global identifications via elements of the corresponding isometry groups. The quantum theory may be viewed as a deformation of this picture, with quantum groups replacing the local isometry groups, and non-commutative spacetimes replacing the classical model spacetimes. This point of view is explained, and open issues are sketched.Comment: Talk given at Geometry and Physics in Cracow, September 2010; 22 pages, 2 figure

Adiabatic dynamics of instantons on S4S ^4

We define and compute the $L^2$ metric on the framed moduli space of circle invariant 1-instantons on the 4-sphere. This moduli space is four dimensional and our metric is $SO(3) \times U(1)$ symmetric. We study the behaviour of generic geodesics and show that the metric is geodesically incomplete. Circle-invariant instantons on the 4-sphere can also be viewed as hyperbolic monopoles, and we interpret our results from this viewpoint. We relate our results to work by Habermann on unframed instantons on the 4-sphere and, in the limit where the radius of the 4-sphere tends to infinity, to results on instantons on Euclidean 4-space.Comment: 49 pages, 11 figures. Significant improvements in the discussion of framing in v

Taub-NUT Dynamics with a Magnetic Field

We study classical and quantum dynamics on the Euclidean Taub-NUT geometry coupled to an abelian gauge field with self-dual curvature and show that, even though Taub-NUT has neither bounded orbits nor quantum bound states, the magnetic binding via the gauge field produces both. The conserved Runge-Lenz vector of Taub-NUT dynamics survives, in a modified form, in the gauged model and allows for an essentially algebraic computation of classical trajectories and energies of quantum bound states. We also compute scattering cross sections and find a surprising electric-magnetic duality. Finally, we exhibit the dynamical symmetry behind the conserved Runge-Lenz and angular momentum vectors in terms of a twistorial formulation of phase space.Comment: 36 pages, three figure

The Minispiral in the Galactic Center revisited

We present the results of a re-examination of a [Ne II] line emission data cube (\lambda 12.8 \mu m) and discuss the kinematic structure of the inner \sim 3 \times 4 pc of the Galaxy. The quality of [Ne II] as a tracer of ionized gas is examined by comparing it to radio data. A three dimensional representation of the data cube allows us to disentangle features which are projected onto the same location on the sky. A model of gas streams in different planes is fitted to the data. We find that most of the material is located in a main plane which itself is defined by the inner edge of the Circum-Nuclear Disk in the Galactic Center. Finally, we present a possible three dimensional model of the gas streams.Comment: 12 pages, 18 figures; submitted to New Astronomy; higher resolution version and two animations available via anonymous ftp ftp://ftp.ita.uni-heidelberg.de/pub/ITA/wjd/Minispira

Activity of Exoenzymes in Treated Wastewater Irrigated Soils

The reuse of reclaimed wastewater for irrigation of agricultural fields greatly influences the activity of soil microorganisms through the input of organic compounds. Due to the production of exoenzymes by microorganisms for the decomposition of substrates it can be assumed that the irrigation with treated wastewater (TWW) has a strong influence on the soil enzyme pool. In this study the activity of ten exoenzymes, which catalyses processes in C, N and P nutrient cycles, were determined in 3 different soils in 0-10, 10-20, 20-30, 30-50, 50-70 and 70-100 cm soil depth. The soils were used for agriculture and irrigated with reclaimed wastewater reused after a secondary treatment step. Additionally a control after freshwater irrigation was studied. Due to the influence of TWW on the soil biology of these soils, also clear effects on soil exoenzymes in freshwater and TWW irrigated soils could be seen. According to Sinsabaugh et al. (2008) we calculated indices which describe the enzymatic resources for acquisition of organic P and organic N relative to C and therefore give insides into the functional convergence of extracellular enzyme activities in soils and the relative nutrient demand. The distribution pattern of these functional enzyme activities varied between freshwater and TWW irrigated soils and shows therefore a strong influence of the TWW irrigation on the activity of exoenzymes. (Sinsabaugh et al. (2008): Stoichiometry of soil enzyme activity at global scale. Ecology Letters 11 (11), 1252-1264.

Classical r-matrices via semidualisation

We study the interplay between double cross sum decompositions of a given Lie algebra and classical r-matrices for its semidual. For a class of Lie algebras which can be obtained by a process of generalised complexification we derive an expression for classical r-matrices of the semidual Lie bialgebra in terms of the data which determines the decomposition of the original Lie algebra. Applied to the local isometry Lie algebras arising in three-dimensional gravity, decomposition and semidualisation yields the main class of non-trivial r-matrices for the Euclidean and Poincare group in three dimensions. In addition, the construction links the r-matrices with the Bianchi classification of three dimensional real Lie algebras.Comment: 21 pages, 1 figure, typos correcte

Jurisdictional Issues: The EEC Merger Control Regulation, Member State Laws, and Articles 85 and 86

This Article deals with two main issues. One is the division of powers between the European Economic Community and the Member States with regard to merger control after September 21, 1990. The other is the possible application, by the Commission of the European Communities or by national authorities, of Article 85 and 86 of the Treaty Establishing the European Economic Community to mergers covered by Regulation No. 4064/89. The Article casts a brief look at how the dividing line between merges and operations which do not qualify as mergers within the sense of article 3 of the Regulation will be treated in the future

Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity

We study the conditions for classical r-matrices to be compatible with the generalised Chern-Simons action for 3d gravity. Compatibility means solving the classical Yang-Baxter equations with a prescribed symmetric part for each of the real Lie algebras and bilinear pairings arising in the generalised Chern-Simons action. We give a new construction of r-matrices via a generalised complexification and derive a non-linear set of matrix equations determining the most general compatible r-matrix. We exhibit new families of solutions and show that they contain known solutions for special parameter valuesComment: 20 pages, minor corrections and comments added in v

Tracing transient charges in expanding clusters

We study transient charges formed in methane clusters following ionization by intense near-infrared laser pulses. Cluster ionization by 400-fs (I=1×1014 W/cm2) pulses is highly efficient, resulting in the observation of a dominant C3+ ion contribution. The C4+ ion yield is very small but is strongly enhanced by applying a time-delayed weak near-infrared pulse. We conclude that most of the valence electrons are removed from their atoms during the laser-cluster interaction and that electrons from the nanoplasma recombine with ions and populate Rydberg states when the cluster expands, leading to a decrease of the average charge state of individual ions. Furthermore, we find clear bound-state signatures in the electron kinetic energy spectrum, which we attribute to Auger decay taking place in expanding clusters. Such nonradiative processes lead to an increase of the final average ion charge state that is measured in experiments. Our results suggest that it is crucial to include both recombination and nonradiative decay processes for the understanding of recorded ion charge spectra