On Lorentz Invariance, Spin-Charge Separation And SU(2) Yang-Mills Theory

Previously it has been shown that in spin-charge separated SU(2) Yang-Mills theory Lorentz invariance can become broken by a one-cocycle that appears in the Lorentz boosts. Here we study in detail the structure of this one-cocycle. In particular we show that its non-triviality relates to the presence of a (Dirac) magnetic monopole bundle. We also explicitely present the finite version of the cocycle.Comment: 4 page

The Biot-Savart operator and electrodynamics on subdomains of the three-sphere

We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integral operator BS acting on all vector fields, we show that electrodynamics in such a setting behaves rather similarly to Euclidean electrodynamics. For instance, for current J and magnetic field BS(J), we show that Maxwell's equations naturally hold. In all instances, the formulas we give are geometrically meaningful: they are preserved by orientation-preserving isometries of the three-sphere. This article describes several properties of BS: we show it is self-adjoint, bounded, and extends to a compact operator on a Hilbert space. For vector fields that act like currents, we prove the curl operator is a left inverse to BS; thus the Biot-Savart operator is important in the study of curl eigenvalues, with applications to energy-minimization problems in geometry and physics. We conclude with two examples, which indicate our bounds are typically within an order of magnitude of being sharp.Comment: 24 pages (was 28 pages) Revised to include a new introduction, a detailed example, and results about helicity; other changes for readabilit

Committee Reports

Contains reports from the following committees of the Washington State Bar Association: Administrative Law, Civil Rights, Code Commission, Cooperation with American Bar Association, Federal Legislation, Improvement of Probate Statutes, Law Examiners, Legal Education, Legal Ethics, Legal Institutes, Legislative, Obituary, Selection of Judges, and Unauthorized Practice of Law. Also includes the auditor\u27s report

UGC 3995: A Close Pair of Spiral Galaxies

UGC 3995 is a close pair of spiral galaxies whose eastern component hosts a Seyfert 2 nucleus. We present a detailed analysis of this system using long slit spectroscopy and narrow (\ha + \nii) as well as broad band (B, R) imaging and an archive WFPC2 image. The component galaxies reveal surprisingly small signs of interaction considering their spatial proximity and almost identical recession velocities, as the bright filament is probably an optical illusion due to the superposition of the bar of the Seyfert galaxy and of the spiral arms of the companion. The broad band morphology, a B--R color map, and a continuum-subtracted \ha + \nii image demonstrate that the western component UGC 3995B is in front of the Seyfert-hosting component UGC 3995A, partly obscuring its western side. The small radial velocity difference leaves the relative motion of the two galaxies largely unconstrained. The observed lack of major tidal deformations, along with some morphological peculiarities, suggests that the galaxies are proximate in space but may have recently approached each other on the plane of the sky. The geometry of the system and the radial velocity curve at P. A. = 106 suggest that the encounter may be retrograde or, alternatively, prograde before perigalacticon. The partial overlap of the two galaxies allows us to estimate the optical thickness of the disk of component B. We derive an extinction = 0.18 visual magnitudes in the infra-arms parts of the foreground galaxy disk, and >= 1-1.5 visual magnitudes in correspondence of the spiral arms.Comment: Accepted for publication in the Astronomical Journal (June 1999 issue

Tidal dwarfs in the M81 group: the second generation?

We derive quantitative star formation histories of the four suspected tidal dwarf galaxies in the M81 group, HolmbergIX, BK3N, Arp-loop (A0952+69), and Garland, using Hubble Space Telescope/Wide Field Planetary Camera2 images in F606W and F814W obtained as part of a Snapshot survey of dwarf galaxies in the Local Universe. We consider the spatial distribution and ages of resolved stellar populations in these dwarf irregular galaxies. We use synthetic color-magnitude diagrams to derive the ages of the major star formation episodes, star formation rates, and approximate metallicity ranges. All the galaxies show evidence of continuous star formation between about 20 and 200 Myr ago with star formation rates in the range 7.5*10^(-3)- 7.6*10^(-4) M(sun)/yr. The metallicity of the detected stars spans a wide range, and have lower than solar abundance. A possible scenario is that all four dwarf galaxies were formed from material in the metal-poor outer part of the giant spiral galaxy M81 after the tidal interaction between M81, M82, and NGC3077 about 200 Myr ago. While we do not directly detect pronounced old stellar populations, the photometric limits of our data are such that the presence of such a population is not entirely ruled out

Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $\Omega_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deformations of (N-1)-dimensional linear subspaces. For the class of solutions which are Laurent polynomials in one variable these systems coincide with N-dimensional integrable systems such as Liouville equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3), dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4) and others. Gauge invariant part of the forms $\Omega_{N-1}$ provides us with the compact form of the corresponding hierarchies. Dual quasi-linear systems associated with the projectively dual Grassmannians Gr(2,N+1) are defined via the requirement of the closedness of the dual forms $\Omega_{N-1}^{\star}$. It is shown that at N=3 the self-dual quasi-linear system, which is associated with the harmonic (closed and co-closed) form $\Omega_{2}$, coincides with the Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde

Observations of Stellar Objects at a Shell Boundary in the Star-Forming Complex in the Galaxy IC1613

The single region of ongoing star formation in the galaxy IC 1613 has been observed in order to reveal the nature of compact emission-line objects at the edges of two shells in the complex, identified earlier in H-alpha line images. The continuum images show these compact objects to be stars. Detailed spectroscopic observations of these stars and the surrounding nebulae were carried out with an integral field spectrograph MPFS mounted on the 6m telescope of the Special Astrophysical Observatory. The resulting stellar spectra were used to determine the spectral types and luminosity classes of the objects. An Of star we identified is the only object of this spectral type in IC 1613. The results of optical observations of the multi-shell complex are compared to 21cm radio observations. The shells harboring the stars at their boundaries constitute the most active part of the star-forming region. There is evidence that shocks have played an important role in the formation of the shells.Comment: 10 pages, 5 PS and 1 color JPEG figur

Non-equilibrium Thermodynamics: Structural Relaxation, Fictive temperature and Tool-Narayanaswamy phenomenology in Glasses

Starting from the second law of thermodynamics applied to an isolated system consisting of the system surrounded by an extremely large medium, we formulate a general non-equilibrium thermodynamic description of the system when it is out of equilibrium. We then apply it to study the structural relaxation in glasses and establish the phenomenology behind the concept of the fictive temperature and of the empirical Tool-Narayanaswamy equation on firmer theoretical foundation.Comment: 20 pages, 1 figur

The Stellar Populations of the Cetus Dwarf Spheroidal Galaxy

We present Hubble Space Telescope Wide Field Planetary Camera 2 photometry in the V and I passbands of the recently discovered Local Group dwarf spheroidal galaxy in Cetus. Our color-magnitude diagram extends from above the first ascent red giant branch (RGB) tip to approximately half a magnitude below the horizontal branch (HB). Adopting a reddening of E(B-V) = 0.03, the magnitude of the RGB tip yields a distance modulus of (m-M)o = 24.46 +/- 0.14. After applying the reddening and distance modulus, we have utilized the color distribution of RGB stars to determine a mean metal abundance of [Fe/H] = -1.7 on the Zinn & West scale with an intrinsic internal abundance dispersion of +/-0.2 dex. An indirect calculation of the HB morphology of Cetus based on the mean dereddened HB color yields (B-R)/(B+V+R) = -0.91 +/- 0.09, which represents an HB that is redder than what can be attributed solely to Cetus' metal abundance. As such, Cetus suffers from the `second parameter effect' in which another parameter besides metallicity is controlling the HB morphology. If we adopt the conventional `age hypothesis' explanation for the second parameter effect, then this implies that Cetus is 2-3 Gyr younger than Galactic globular clusters at its metallicity.Comment: 13 pages, 8 figures, Accepted for publication in the March 10, 2002 Ap