Spectral Action for Robertson-Walker metrics

We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our previous method of computation of the spectral action based on the Poisson summation formula. We show how to compute directly the spectral action for the general case of Robertson-Walker metrics. We check the terms of the expansion up to a_6 against the known universal formulas of Gilkey and compute the expansion up to a_{10} using our direct method

Ice nucleation efficiency of natural dust samples in the immersion mode

A total of 12 natural surface dust samples, which were surface-collected on four continents, most of them in dust source regions, were investigated with respect to their ice nucleation activity. Dust collection sites were distributed across Africa, South America, the Middle East, and Antarctica. Mineralogical composition has been determined by means of X-ray diffraction. All samples proved to be mixtures of minerals, with major contributions from quartz, calcite, clay minerals, K-feldspars, and (Na, Ca)-feldspars. Reference samples of these minerals were investigated with the same methods as the natural dust samples. Furthermore, Arizona test dust (ATD) was re-evaluated as a benchmark. Immersion freezing of emulsion and bulk samples was investigated by differential scanning calorimetry. For emulsion measurements, water droplets with a size distribution peaking at about 2 µm, containing different amounts of dust between 0.5 and 50 wt % were cooled until all droplets were frozen. These measurements characterize the average freezing behaviour of particles, as they are sensitive to the average active sites present in a dust sample. In addition, bulk measurements were conducted with one single 2 mg droplet consisting of a 5 wt % aqueous suspension of the dusts/minerals. These measurements allow the investigation of the best ice-nucleating particles/sites available in a dust sample. All natural dusts, except for the Antarctica and ATD samples, froze in a remarkably narrow temperature range with the heterogeneously frozen fraction reaching 10 % between 244 and 250 K, 25 % between 242 and 246 K, and 50 % between 239 and 244 K. Bulk freezing occurred between 255 and 265 K. In contrast to the natural dusts, the reference minerals revealed ice nucleation temperatures with 2–3 times larger scatter. Calcite, dolomite, dolostone, and muscovite can be considered ice nucleation inactive. For microcline samples, a 50 % heterogeneously frozen fraction occurred above 245 K for all tested suspension concentrations, and a microcline mineral showed bulk freezing temperatures even above 270 K. This makes microcline (KAlSi3O8) an exceptionally good ice-nucleating mineral, superior to all other analysed K-feldspars, (Na, Ca)-feldspars, and the clay minerals. In summary, the mineralogical composition can explain the observed freezing behaviour of 5 of the investigated 12 natural dust samples, and partly for 6 samples, leaving the freezing efficiency of only 1 sample not easily explained in terms of its mineral reference components. While this suggests that mineralogical composition is a major determinant of ice-nucleating ability, in practice, most natural samples consist of a mixture of minerals, and this mixture seems to lead to remarkably similar ice nucleation abilities, regardless of their exact composition, so that global models, in a first approximation, may represent mineral dust as a single species with respect to ice nucleation activity. However, more sophisticated representations of ice nucleation by mineral dusts should rely on the mineralogical composition based on a source scheme of dust emissions

Open string theory and planar algebras

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the well known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure

Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory

We show that the simplest non commutative renormalizable field theory, the $\phi^4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe to all orders in perturbation theor

Feynman graph polynomials

The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.Comment: 35 pages, references adde

Spin Foams and Noncommutative Geometry

We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure

The spectral action and cosmic topology

The spectral action functional, considered as a model of gravity coupled to matter, provides, in its non-perturbative form, a slow-roll potential for inflation, whose form and corresponding slow-roll parameters can be sensitive to the underlying cosmic topology. We explicitly compute the non-perturbative spectral action for some of the main candidates for cosmic topologies, namely the quaternionic space, the Poincare' dodecahedral space, and the flat tori. We compute the corresponding slow-roll parameters and see we check that the resulting inflation model behaves in the same way as for a simply-connected spherical topology in the case of the quaternionic space and the Poincare' homology sphere, while it behaves differently in the case of the flat tori. We add an appendix with a discussion of the case of lens spaces.Comment: 55 pages, LaTe

Noncommutative spectral geometry, dissipation and the origin of quantization

We present a physical interpretation of the doubling of the algebra, which is the basic ingredient of the noncommutative spectral geometry, developed by Connes and collaborators as an approach to unification. We discuss its connection to dissipation and to the gauge structure of the theory. We then argue, following 't Hooft's conjecture, that noncommutative spectral geometry classical construction carries implicit in its feature of the doubling of the algebra the seeds of quantization.Comment: 9 pages, to appear in the Proceedings of the international conference "Emergent Quantum Mechanics (EmerQuM11)", November 11-13, 2011, University of Vienn

On Spectral Triples in Quantum Gravity II

A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two papers on the subject.Comment: 43 pages, 1 figur

Cluster analysis of the organic peaks in bulk mass spectra obtained during the 2002 New England Air Quality Study with an Aerodyne aerosol mass spectrometer

International audienceWe applied hierarchical cluster analysis to an Aerodyne aerosol mass spectrometer (AMS) bulk mass spectral dataset collected aboard the NOAA research vessel Ronald H. Brown during the 2002 New England Air Quality Study off the east coast of the United States. Emphasizing the organic peaks, the cluster analysis yielded a series of categories that are distinguishable with respect to their mass spectra and their occurrence as a function of time. The differences between the categories mainly arise from relative intensity changes rather than from the presence or absence of specific peaks. The most frequent category exhibits a strong signal at m/z 44 and represents oxidized organic matter most probably originating from both, anthropogenic as well as biogenic sources. On the basis of spectral and trace gas correlations, the second most common category with strong signals at m/z 29, 43, and 44 contains contributions from isoprene oxidation products. The third through the fifth most common categories have peak patterns characteristic of monoterpene oxidation products and were most frequently observed when air masses from monoterpene rich regions were sampled. Taken together, the second through the fifth most common categories represent as much as 5 µg/m3 organic aerosol mass ? 17% of the total organic mass ? that can be attributed to biogenic sources. These numbers have to be viewed as lower limits since the most common category was attributed to anthropogenic sources for this calculation. The cluster analysis was also very effective in identifying a few contaminated mass spectra that were not removed during pre-processing. This study demonstrates that hierarchical clustering is a useful tool to analyze the complex patterns of the organic peaks in bulk aerosol mass spectra from a field study