The Stellar Composition of the Star Formation Region CMa R1. II. Spectroscopic and Photometric Observations of 9 Young Stars

We present new high and low resolution spectroscopic and photometric data of nine members of the young association CMa R1. All the stars have circumstellar dust at some distance as could be expected from their association with reflection nebulosity. Four stars (HD 52721, HD 53367, LkHalpha 220 and LkHalpha 218) show Halpha emission and we argue that they are Herbig Be stars with discs. Our photometric and spectroscopic observations on these stars reveal new characteristics of their variability. We present first interpretations of the variability of HD 52721, HD 53367 and the two LkHalpha stars in terms of a partially eclipsing binary, a magnetic activity cycle and circumstellar dust variations, respectively. The remaining five stars show no clear indications of Halpha emission in their spectra, although their spectral types and ages are comparable with those of HD 52721 and HD 53367. This indicates that the presence of a disc around a star in CMa R1 may depend on the environment of the star. In particular we find that all Halpha emission stars are located at or outside the arc-shaped border of the H II region, which suggests that the stars inside the arc have lost their discs through evaporation by UV photons from nearby O stars, or from the nearby (< 25 pc) supernova, about 1 Myr ago.Comment: 17 pages, 13 figures, accepted by MNRA

Representation theory of finite W algebras

In this paper we study the finitely generated algebras underlying $W$ algebras. These so called 'finite $W$ algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of $sl_2$ into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite $W$ algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite $W$ symmetry. In the second part we BRST quantize the finite $W$ algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite $W$ algebras in one stroke. Explicit results for $sl_3$ and $sl_4$ are given. In the last part of the paper we study the representation theory of finite $W$ algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finite $W$ algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite $W$ algebras.Comment: 62 pages, THU-92/32, ITFA-28-9

Supersymmetric structure of the induced W gravities

We derive the supersymmetric structure present in W-gravities which has been already observed in various contexts as Yang-Mills theory, topological field theories, bosonic string and chiral W_{3}-gravity. This derivation which is made in the geometrical framework of Zucchini, necessitates the introduction of an appropriate new basis of variables which replace the canonical fields and their derivatives. This construction is used, in the W_{2}-case, to deduce from the Chern-Simons action the Wess-Zumino-Polyakov action.Comment: 17 pages, Latex. To appear in Class. Quantum. Gravit

Vortices on Higher Genus Surfaces

We consider the topological interactions of vortices on general surfaces. If the genus of the surface is greater than zero, the handles can carry magnetic flux. The classical state of the vortices and the handles can be described by a mapping from the fundamental group to the unbroken gauge group. The allowed configurations must satisfy a relation induced by the fundamental group. Upon quantization, the handles can carry ``Cheshire charge.'' The motion of the vortices can be described by the braid group of the surface. How the motion of the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint CALT-68-187

Lagrangian and Hamiltonian Formalism on a Quantum Plane

We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle coordinates and velocities. Using techniques similar to those of Wess and Zumino, we construct two different differential calculi on $TQ_{q,p}$. These two differential calculi can in principle give rise to two different particle dynamics, starting from a single Lagrangian. For Hamiltonian mechanics, we define a phase space $T^*Q_{q,p}$ spanned by noncommuting particle coordinates and momenta. The commutation relations for the momenta can be determined only after knowing their functional dependence on coordinates and velocities. Thus these commutation relations, as well as the differential calculus on $T^*Q_{q,p}$, depend on the initial choice of Lagrangian. We obtain the deformed Hamilton's equations of motion and the deformed Poisson brackets, and their definitions also depend on our initial choice of Lagrangian. We illustrate these ideas for two sample Lagrangians. The first system we examine corresponds to that of a nonrelativistic particle in a scalar potential. The other Lagrangian we consider is first order in time derivative

The Stellar Composition of the Star Formation Region CMa R1 -- III. A new outburst of the Be star component in Z CMa

We report on a recent event in which, after more than a decade of slowly fading, the visual brightness of the massive young binary Z CMa suddenly started to rise by about 1 magnitude in December 1999, followed by a rapid decline to its previous brightness over the next six months. This behaviour is similar to that exhibited by this system around its eruption in February 1987. A comparison of the intrinsic luminosities of the system with recent evolutionary calculations shows that Z CMa may consist of a 16 M_sun B0 IIIe primary star and a ~ 3 M_sun FUOr secondary with a common age of ~ 3 x 10^5 yr. We also compare new high-resolution spectra obtained in Jan. and Feb. 2000, during the recent rise in brightness, with archive data from 1991 and 1996. The spectra are rich in emission lines, which originate from the envelope of the early B-type primary star. The strength of these emission lines increased strongly with the brightness of Z CMa. We interpret the collected spectral data in terms of an accretion disc with atmosphere around the Herbig B0e component of Z CMa, which has expanded during the outbursts of 1987 and 2000. A high resolution profile of the 6300 A [O I] emission line, obtained by us in March 2002 shows an increase in flux and a prominent blue shoulder to the feature extending to ~ -700 km/s, which was much fainter in the pre-outburst spectra. We propose that this change in profile is a result of a strong change in the collimation of a jet, as a result of the outburst at the start of this century.Comment: 22 pages, 12 figures, accepted for publication in MNRA

On realizations of nonlinear Lie algebras by differential operators

We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear, quadratic and cubic cases are explicitly visited but the method works for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are studied in the context of these ``nonlinear'' Lie algebras and some examples dealing with quantum optics are pointed out.Comment: 21 pages, Latex; New examples added in Sect.

Contractions, deformations and curvature

The role of curvature in relation with Lie algebra contractions of the pseudo-ortogonal algebras so(p,q) is fully described by considering some associated symmetrical homogeneous spaces of constant curvature within a Cayley-Klein framework. We show that a given Lie algebra contraction can be interpreted geometrically as the zero-curvature limit of some underlying homogeneous space with constant curvature. In particular, we study in detail the contraction process for the three classical Riemannian spaces (spherical, Euclidean, hyperbolic), three non-relativistic (Newtonian) spacetimes and three relativistic ((anti-)de Sitter and Minkowskian) spacetimes. Next, from a different perspective, we make use of quantum deformations of Lie algebras in order to construct a family of spaces of non-constant curvature that can be interpreted as deformations of the above nine spaces. In this framework, the quantum deformation parameter is identified as the parameter that controls the curvature of such "quantum" spaces.Comment: 17 pages. Based on the talk given in the Oberwolfach workshop: Deformations and Contractions in Mathematics and Physics (Germany, january 2006) organized by M. de Montigny, A. Fialowski, S. Novikov and M. Schlichenmaie

A spectroscopic survey of Herbig Ae/Be stars with X-shooter – I. Stellar parameters and accretion rates

Herbig Ae/Be stars (HAeBes) span a key mass range that links low- and high-mass stars, and thus provide an ideal window from which to explore their formation. This paper presents Very Large Telescope/X-shooter spectra of 91 HAeBes, the largest spectroscopic study of HAeBe accretion to date. A homogeneous approach to determining stellar parameters is undertaken for the majority of the sample. Measurements of the ultraviolet are modelled within the context of magnetospheric accretion, allowing a direct determination of mass accretion rates. Multiple correlations are observed across the sample between accretion and stellar properties: the youngest and often most massive stars are the strongest accretors, and there is an almost 1:1 relationship between the accretion luminosity and stellar luminosity. Despite these overall trends of increased accretion rates in HAeBes when compared to classical T Tauri stars, we also find noticeable differences in correlations when considering the Herbig Ae and Herbig Be subsets. This, combined with the difficulty in applying a magnetospheric accretion model to some of the Herbig Be stars, could suggest that another form of accretion may be occurring within Herbig Be mass range