Gipsy 3D: Analysis, Visualization and Vo-Tools

The scientific goals of the AMIGA project are based on the analysis of a significant amount of spectroscopic 3D data. In order to perform this work we present an initiative to develop a new VO compliant package, including present core applications and tasks offered by the Groningen Image Processing System (GIPSY), and new ones based on use cases elaborated in collaboration with ad- vanced users. One of the main goals is to provide local interoperability between GIPSY (visualization and data analysis) and other VO software. The connectivity with the Virtual Observatory environment will provide general access to 3D data VO archives and services, maximizing the potential for scientific discovery.Comment: 2 pages, 1 figure, to appear in the proceedings of the "Multi-wavelength Astronomy and Virtual Observatory" Workshop held at ESAC 1-3 Dec 200

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Morpho-kinematical modelling in the molecular zoo beyond CO: the case of M 1-92

Ongoing improvements of sub-mm- and mm-range interferometers and single-dish radiotelescopes are progressively allowing the detailed study of planetary nebulae (PNe) in molecular species other than 12CO and 13CO. We are implementing a new set of tables for extending the capabilities of the morpho-kinematical modelling tool SHAPE+shapemol, so radiative transfer in molecular species beyond 12CO and 13CO, namely C17O, C18O, HCN, HNC, CS, SiO, HCO+, and N2H+, are enabled under the Large Velocity Gradient approximation with the ease of use of SHAPE. We present preliminary results on the simultaneous analysis of a plethora of IRAM-30m and HERSCHEL/HIFI spectra, and NOEMA maps of different species in the pre-PN nebula M~1-92, which show interesting features such as a previously undetected pair of polar, turbulent, high-temperature blobs, or a 17O/18O isotopic ratio of 1.7, which indicates the AGB should have turned C-rich, as opposed to the apparent nature of its O-rich nebula.Comment: To be published in the Proceedings of the IAU Symposium 384; 6 pages, 5 figures, 1 tabl

Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Non-standard quantum so(3,2) and its contractions

A full (triangular) quantum deformation of so(3,2) is presented by considering this algebra as the conformal algebra of the 2+1 dimensional Minkowskian spacetime. Non-relativistic contractions are analysed and used to obtain quantum Hopf structures for the conformal algebras of the 2+1 Galilean and Carroll spacetimes. Relations between the latter and the null-plane quantum Poincar\'e algebra are studied.Comment: 9 pages, LaTe

The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these `curved' harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK) type approach, with two free parameters \ki, \kii which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere ${\bf S}^2$, hyperbolic plane ${\bf H}^2$, AntiDeSitter sphere {\bf AdS}^{\unomasuno} and DeSitter sphere {\bf dS}^{\unomasuno}) appear in this family, with the Euclidean and Minkowski spaces as flat limits. We solve the equations of motion for the `curved' harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: first by direct integration, second by obtaining the general CK version of the Binet's equation and third, as a consequence of its superintegrable character. The orbits are conics with centre at the potential origin in any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents those results of the theory of conics on spaces of constant curvature which are pertinent.Comment: 29 pages, 6 figure

Momentum dependence of the superconducting gap in NdFeAsO1-xFx single crystals measured by angle resolved photoemission spectroscopy

We use angle resolved photoemission spectroscopy (ARPES) to study the momentum dependence of the superconducting gap in NdFeAsO1-xFx single crystals. We find that the Gamma hole pocket is fully gapped below the superconducting transition temperature. The value of the superconducting gap is 15 +- 1.5 meV and its anisotropy around the hole pocket is smaller than 20% of this value. This is consistent with an isotropic or anisotropic s-wave symmetry of the order parameter or exotic d-wave symmetry with nodes located off the Fermi surface sheets. This is a significant departure from the situation in the cuprates, pointing to possibility that the superconductivity in the iron arsenic based system arises from a different mechanism.Comment: 4 pages, 3 figure

Spectrum Generating Algebras for the free motion in S3S^3

We construct the spectrum generating algebra (SGA) for a free particle in the three dimensional sphere $S^3$ for both, classical and quantum descriptions. In the classical approach, the SGA supplies time-dependent constants of motion that allow to solve algebraically the motion. In the quantum case, the SGA include the ladder operators that give the eigenstates of the free Hamiltonian. We study this quantum case from two equivalent points of view.Comment: 29 pages, 1 figur

Maximal superintegrability on N-dimensional curved spaces

A unified algebraic construction of the classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie groups SO(N+1), ISO(N), and SO(N,1) is presented. Firstly, general expressions for the Hamiltonian and its integrals of motion are given in a linear ambient space $R^{N+1}$, and secondly they are expressed in terms of two geodesic coordinate systems on the ND spaces themselves, with an explicit dependence on the curvature as a parameter. On the sphere, the potential is interpreted as a superposition of N+1 oscillators. Furthermore each Lie algebra generator provides an integral of motion and a set of 2N-1 functionally independent ones are explicitly given. In this way the maximal superintegrability of the ND Euclidean Smorodinsky-Winternitz system is shown for any value of the curvature.Comment: 8 pages, LaTe