1,125 research outputs found
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 starting from the one corresponding to . 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 . All Lie bialgebra contractions studied in this paper define
Hopf algebra contractions for the Drinfel'd-Jimbo deformations .
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 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
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