Infinitesimal deformation quantization of complex analytic spaces

Global constructions of quantization deformation and obstructions are discussed for an arbitrary complex analytic space in terms of adapted (analytic) Hochschild cohomology. For K3-surfaces an explicit global construction of a Poisson bracket is given. It is shown that the analytic Hochschild (co)homology on a complex space has structure of coherent analytic sheaf in each degree

Hopf algebras: motivations and examples

This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual

Combinatorial Hopf algebras in quantum field theory I

This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as well an elementary invitation to the subject. The rest of part I, comprising Sections 2-6, is devoted to the basics of Hopf algebra theory and examples, in ascending level of complexity. Part II turns around the all-important Faa di Bruno Hopf algebra. Section 7 contains a first, direct approach to it. Section 8 gives applications of the Faa di Bruno algebra to quantum field theory and Lagrange reversion. Section 9 rederives the related Connes-Moscovici algebras. In Part III we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Section10 we describe the first. Then in Section11 we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Section 12 general incidence algebras are introduced, and the Faa di Bruno bialgebras are described as incidence bialgebras. In Section 13, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained; this is the heart of the paper. The structure results for commutative Hopf algebras are found in Sections 14 and 15. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.Comment: 94 pages, LaTeX figures, precisions made, typos corrected, more references adde

Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups

Given a group automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that any irreducible lattice in a connected semi simple Lie group having finite centre and rank at least 2 has the $R_\infty$-property.Comment: 6 page

ARIS-Campaign: intercomparison of three ground based 22 GHz radiometers for middle atmospheric water vapor at the Zugspitze in winter 2009

This paper presents the Alpine Radiometer Intercomparison at the Schneefernerhaus (ARIS), which took place in winter 2009 at the high altitude station at the Zugspitze, Germany (47.42° N, 10.98° E, 2650 m). This campaign was the first direct intercomparison between three new ground based 22 GHz water vapor radiometers for middle atmospheric profiling with the following instruments participating: MIRA 5 (Karlsruhe Institute of Technology), cWASPAM3 (Max Planck Institute for Solar System Research, Katlenburg-Lindau) and MIAWARA-C (Institute of Applied Physics, University of Bern). Even though the three radiometers all measure middle atmospheric water vapor using the same rotational transition line and similar fundamental set-ups, there are major differences between the front ends, the back ends, the calibration concepts and the profile retrieval. The spectrum comparison shows that all three radiometers measure spectra without severe baseline artifacts and that the measurements are in good general agreement. The measurement noise shows good agreement to the values theoretically expected from the radiometer noise formula. At the same time the comparison of the noise levels shows that there is room for instrumental and calibration improvement, emphasizing the importance of low elevation angles for the observation, a low receiver noise temperature and an efficient calibration scheme. <br><br> The comparisons of the retrieved profiles show that the agreement between the profiles of MIAWARA-C and cWASPAM3 with the ones of MLS is better than 0.3 ppmv (6%) at all altitudes. MIRA 5 has a dry bias of approximately 0.5 ppm (8%) below 0.1 hPa with respect to all other instruments. The profiles of cWASPAM3 and MIAWARA-C could not be directly compared because the vertical region of overlap was too small. The comparison of the time series at different altitude levels show a similar evolution of the H<sub>2</sub>O volume mixing ratio (VMR) for the ground based instruments as well as the space borne sensor MLS

House price Keynesianism and the contradictions of the modern investor subject

This article conceptualises the marked downturn in UK house prices in the 2007-2009 period in relation to longer-term processes of national economic restructuring centred on a new model of homeownership. The structure of UK house prices has been impacted markedly by the Labour Government‟s efforts to ingrain a particular notion of financial literacy amid the move towards an increasingly asset-based system of welfare. New model welfare recipients and new model homeowners have thereby been co-constituted in a manner consistent with a new UK growth regime of „house price Keynesianism‟. However, the investor subjects who drive such growth are necessarily rendered uncertain as compared with the idealised image of Government policy because of their reliance on the credit-creating decisions of private financial institutions. The recent steep decline in UK house prices is explained here as an epiphenomenon of the disruptive effect on the idealised image caused by the dependence of investor subjects on pricing dynamics not of their making

Long-term in situ observations of biomass burning aerosol at a high altitude station in Venezuela – sources, impacts and interannual variability

First long-term observations of South American biomass burning aerosol within the tropical lower free troposphere are presented. The observations were conducted between 2007 and 2009 at a high altitude station (4765 m a.s.l.) on the Pico Espejo, Venezuela. Sub-micron aerosol volume, number concentrations of primary particles and particle absorption were observed. Orographic lifting and shallow convection leads to a distinct diurnal cycle at the station. It enables measurements within the lower free troposphere during night time and observations of boundary layer air masses during day time and at their transitional regions. The seasonal cycle is defined by a wet rainy season and a dry biomass burning season. The particle load of biomass burning aerosol is dominated by fires in the Venezuelan savannah. Increases of aerosol concentrations could not be linked to long-range transport of biomass burning plumes from the Amazon basin or Africa due to effective wet scavenging of particles. Highest particle concentrations were observed within boundary layer air masses during the dry season. Ambient sub-micron aerosol volume reached 1.4 ± 1.3 μm³ cm^−3, heated (300 °C) particle number concentrations 510 ± 420 cm^−3 and the absorption coefficient 0.91 ± 1.2 Mm^−1. The respective concentrations were lowest within the lower free troposphere during the wet season and averaged at 0.19 ± 0.25 μm³ cm^−3, 150 ± 94 cm^−3 and 0.15 ± 0.26 Mm^−1. A decrease of particle concentrations during the dry seasons from 2007–2009 could be connected to a decrease in fire activity in the wider region of Venezuela using MODIS satellite observations. The variability of biomass burning is most likely linked to the El Niño-Southern Oscillation (ENSO). Low biomass burning activity in the Venezuelan savannah was observed to follow La Niña conditions, high biomass burning activity followed El Niño conditions