Remarks on the representation theory of the Moyal plane

We present an explicit construction of a unitary representation of the commutator algebra satisfied by position and momentum operators on the Moyal plane.Comment: 10 pages, minor changes, refs. adde

Ricci flow, quantum mechanics and gravity

It has been argued that, underlying any given quantum-mechanical model, there exists at least one deterministic system that reproduces, after prequantisation, the given quantum dynamics. For a quantum mechanics with a complex d-dimensional Hilbert space, the Lie group SU(d) represents classical canonical transformations on the projective space CP^{d-1} of quantum states. Let R stand for the Ricci flow of the manifold SU(d-1) down to one point, and let P denote the projection from the Hopf bundle onto its base CP^{d-1}. Then the underlying deterministic model we propose here is the Lie group SU(d), acted on by the operation PR. Finally we comment on some possible consequences that our model may have on a quantum theory of gravity.Comment: 8 page

On the noncommutative eikonal

We study the eikonal approximation to quantum mechanics on the Moyal plane. Instead of using a star product, the analysis is carried out in terms of operator-valued wavefunctions depending on noncommuting, operator-valued coordinates.Comment: 18 page

Through the magnifying glass: ALMA acute viewing of the intricate nebular architecture of OH231.8+4.2

We present continuum and molecular line emission ALMA observations of OH 231.8+4.2, a well studied bipolar nebula around an asymptotic giant branch (AGB) star. The high angular resolution (~0.2-0.3 arcsec) and sensitivity of our ALMA maps provide the most detailed and accurate description of the overall nebular structure and kinematics of this object to date. We have identified a number of outflow components previously unknown. Species studied in this work include 12CO, 13CO, CS, SO, SO2, OCS, SiO, SiS, H3O+, Na37Cl, and CH3OH. The molecules Na37Cl and CH3OH are first detections in OH 231.8+4.2, with CH3OH being also a first detection in an AGB star. Our ALMA maps bring to light the totally unexpected position of the mass-losing AGB star (QX Pup) relative to the large-scale outflow. QX Pup is enshrouded within a compact (<60 AU) parcel of dust and gas (clump S) in expansion (V~5-7 km/s) that is displaced by 0.6arcsec to the south of the dense equatorial region (or waist) where the bipolar lobes join. Our SiO maps disclose a compact bipolar outflow that emerges from QX Pup's vicinity. This outflow is oriented similarly to the large-scale nebula but the expansion velocities are about ten times lower (~35 km/s). We deduce short kinematical ages for the SiO outflow, ranging from ~50-80 yr, in regions within ~150 AU, to ~400-500 yr at the lobe tips (~3500 AU). Adjacent to the SiO outflow, we identify a small-scale hourglass-shaped structure (mini-hourglass) that is probably made of compressed ambient material formed as the SiO outflow penetrates the dense, central regions of the nebula. The lobes and the equatorial waist of the mini-hourglass are both radially expanding with a constant velocity gradient. The mini-waist is characterized by extremely low velocities, down to ~1 km/s at ~150 AU, which tentatively suggest the presence of a stable structure. (abridged

Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras $so(p,q)$ starting from the one corresponding to $so(N+1)$. It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases $N=2,3,4$. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel'd-Jimbo deformations $U_z so(p,q)$. They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincar\'e and Galilean algebras.Comment: 26 pages LATE

Effects of the environment on galaxies in the Catalogue of Isolated Galaxies: physical satellites and large scale structure

We aim to identify and quantify the effects of the satellite distribution around a sample of galaxies in the Catalogue of Isolated Galaxies (CIG), as well as the effects of the Large Scale Structure (LSS) using the SDSS-DR9. To recover the physically bound galaxies we focus on the satellites which are within the escape speed of each CIG galaxy. We also propose a more conservative method using the stacked Gaussian distribution of the velocity difference of the neighbours. The tidal strengths affecting the primary galaxy are estimated to quantify the effects of the local and LSS environments. We also define the projected number density parameter at the 5$^{\rm th}$ nearest neighbour to characterise the LSS around the CIG galaxies. Out of the 386 CIG galaxies considered in this study, at least 340 (88\% of the sample) have no physically linked satellite. Out of the 386 CIG galaxies, 327 (85\% of the sample) have no physical companion within a projected distance of 0.3 Mpc. The CIG galaxies are distributed following the LSS of the local Universe, although presenting a large heterogeneity in their degree of connection with it. A clear segregation appears between early-type CIG galaxies with companions and isolated late-type CIG galaxies. Isolated galaxies are in general bluer, with likely younger stellar populations and rather high star formation with respect to older, redder CIG galaxies with companions. Reciprocally, the satellites are redder and with an older stellar populations around massive early-type CIG galaxies, while they have a younger stellar content around massive late-type CIG galaxies. This suggests that the CIG is composed of a heterogeneous population of galaxies, sampling from old to more recent, dynamical systems of galaxies.Comment: 19 pages, 10 figures, 1 table, accepted for publication in Astronomy & Astrophysic