Three Dimensional Quantum Geometry and Deformed Poincare Symmetry

We study a three dimensional non-commutative space emerging in the context of three dimensional Euclidean quantum gravity. Our starting point is the assumption that the isometry group is deformed to the Drinfeld double D(SU(2)). We generalize to the deformed case the construction of the flat Euclidean space as the quotient of its isometry group ISU(2) by SU(2). We show that the algebra of functions becomes the non-commutative algebra of SU(2) distributions endowed with the convolution product. This construction gives the action of ISU(2) on the algebra and allows the determination of plane waves and coordinate functions. In particular, we show that: (i) plane waves have bounded momenta; (ii) to a given momentum are associated several SU(2) elements leading to an effective description of an element in the algebra in terms of several physical scalar fields; (iii) their product leads to a deformed addition rule of momenta consistent with the bound on the spectrum. We generalize to the non-commutative setting the local action for a scalar field. Finally, we obtain, using harmonic analysis, another useful description of the algebra as the direct sum of the algebra of matrices. The algebra of matrices inherits the action of ISU(2): rotations leave the order of the matrices invariant whereas translations change the order in a way we explicitly determine.Comment: latex, 37 page

Colourful Poincaré symmetry, gravity and particle actions

We construct a generalisation of the three-dimensional Poincar\'e algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincar\'e gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincar\'e symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory

ISO LWS Spectra of T Tauri and Herbig AeBe stars

We present an analysis of ISO-LWS spectra of eight T Tauri and Herbig AeBe young stellar objects. Some of the objects are in the embedded phase of star-formation, whereas others have cleared their environs but are still surrounded by a circumstellar disk. Fine-structure lines of [OI] and [CII] are most likely excited by far-ultraviolet photons in the circumstellar environment rather than high-velocity outflows, based on comparisons of observed line strengths with predictions of photon-dominated and shock chemistry models. A subset of our stars and their ISO spectra are adequately explained by models constructed by Chiang & Goldreich (1997) and Chiang et al. (2001) of isolated, passively heated, flared circumstellar disks. For these sources, the bulk of the LWS flux at wavelengths longward of 55 µm arises from the disk interior which is heated diffusively by reprocessed radiation from the disk surface. At 45 µm, water ice emission bands appear in spectra of two of the coolest stars, and are thought to arise from icy grains irradiated by central starlight in optically thin disk surface layers

Spectral Energy Distributions of T Tauri and Herbig Ae Disks: Grain Mineralogy, Parameter Dependences, and Comparison with ISO LWS Observations

We improve upon the radiative, hydrostatic equilibrium models of passive circumstellar disks constructed by Chiang & Goldreich (1997). New features include (1) account for a range of particle sizes, (2) employment of laboratory-based optical constants of representative grain materials, and (3) numerical solution of the equations of radiative and hydrostatic equilibrium within the original 2-layer (disk surface + disk interior) approximation. We explore how the spectral energy distribution (SED) of a face-on disk depends on grain size distributions, disk geometries and surface densities, and stellar photospheric temperatures. Observed SEDs of 3 Herbig Ae and 2 T Tauri stars, including spectra from the Long Wavelength Spectrometer (LWS) aboard the Infrared Space Observatory (ISO), are fitted with our models. Silicate emission bands from optically thin, superheated disk surface layers appear in nearly all systems. Water ice emission bands appear in LWS spectra of 2 of the coolest stars. Infrared excesses in several sources are consistent with vertical settling of photospheric grains. While this work furnishes further evidence that passive reprocessing of starlight by flared disks adequately explains the origin of infrared-to-millimeter wavelength excesses of young stars, we emphasize how the SED alone does not provide sufficient information to constrain particle sizes and disk masses uniquely.Comment: Accepted to ApJ, 35 pages inc. 14 figures, AAS preprin

A Note on B-observables in Ponzano-Regge 3d Quantum Gravity

We study the insertion and value of metric observables in the (discrete) path integral formulation of the Ponzano-Regge spinfoam model for 3d quantum gravity. In particular, we discuss the length spectrum and the relation between insertion of such B-observables and gauge fixing in the path integral.Comment: 17 page

Motion in Quantum Gravity

We tackle the question of motion in Quantum Gravity: what does motion mean at the Planck scale? Although we are still far from a complete answer we consider here a toy model in which the problem can be formulated and resolved precisely. The setting of the toy model is three dimensional Euclidean gravity. Before studying the model in detail, we argue that Loop Quantum Gravity may provide a very useful approach when discussing the question of motion in Quantum Gravity.Comment: 30 pages, to appear in the book "Mass and Motion in General Relativity", proceedings of the C.N.R.S. School in Orleans, France, eds. L. Blanchet, A. Spallicci and B. Whitin

Duality and Braiding in Twisted Quantum Field Theory

We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are covariant under the duality.Comment: 35 pages; v2: Typos correcte

Chondrule Formation and Protoplanetary Disk Heating by Current Sheets in Non-Ideal Magnetohydrodynamic Turbulence

We study magnetic field steepening due to ambipolar diffusion (Brandenburg & Zweibel 1994) in protoplanetary disk environments and draw the following conclusions. Current sheets are generated in magnetically active regions of the disk where the ionization fraction is high enough for the magnetorotational instability to operate. In late stages of solar nebula evolution, the surface density is expected to have lowered and dust grains to have gravitationally settled to the midplane. If the local dust-to-gas mass ratio near the midplane is increased above cosmic abundances by factors > 10^3, current sheets reach high enough temperatures to melt millimeter-sized dust grains, and hence may provide the mechanism to form meteoritic chondrules. In addition, these current sheets possibly explain the near-infrared excesses observed in spectral energy distributions (SEDs) of young stellar objects. Direct imaging of protoplanetary disks via a nulling interferometer or, in the future, a multi-band, adaptive optics coronagraph can test this hypothesis.Comment: 11 pages, 4 figures, submitted to Ap