Some Observations on Non-covariant Gauges and the epsilon-term

We consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. From rather elementary considerations, we demonstrate the necessity of inclusion of an epsilon-term (even) in the formal treatments, without which one may reach incorrect conclusions. We show, further, that the epsilon-term can contribute to the BRST WT-identities in a nontrivial way (even as epsilon-->0). We also show that the (expectation value of the) correct epsilon-term satisfies an algebraic condition. We show by considering (a commonly used) example of a simple local quadratic epsilon -term, that they lead to additional constraints on Green's function that are not normally taken into account in the BRST formalism that ignores the epsilon-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that for a subclass of these gauges, the Minkowski path-integral could not be obtained by a Wick rotation from a Euclidean path-integral.Comment: 12 pages, LaTeX2

The identification of physical close galaxy pairs

A classification scheme for close pairs of galaxies is proposed. The scheme is motivated by the fact that the majority of apparent close pairs are in fact wide pairs in three-dimensional space. This is demonstrated by means of numerical simulations of random samples of binary galaxies and the scrutiny of the resulting projected and spatial separation distributions. Observational strategies for classifying close pairs according to the scheme are suggested. As a result, physical (i.e., bound and spatially) close pairs are identified.Comment: 16 pages, 5 figures, accepted for publication in The Astronomical Journal, added text corrections on proof

Polarization quadrature measurement of subwavelength diffracting structures

The amplitude and the phase of the diffracted far field depends on polarization when the diffracting structure is comparable to or less than the wavelength. When the far-field amplitude and the phase of one polarization with respect to the orthogonal polarization is measured, small changes in the structure can be measured. To make the far-field polarization measurements, we design a detector that measures the relative polarization amplitude and the phase in quadrature. We predict numerically and verify experimentally the polarization amplitude and the phase for an optical disc and a set of gratings with varying depth. Our results show that this measurement technique is sensitive to small variations in the diffracting structure and that it can be useful in applications such as critical dimension and overlay metrology in microelectronics fabrication

An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems

In the context of analyzing a new model for nonlinear diffusion in polymers, an unusual condition appears at the moving interface between the glassy and rubbery phases of the polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our equations, has received very little attention in the mathematical literature. Due to the unusual form of the moving-boundary condition, further study is needed as to the existence and uniqueness of solutions satisfying such a condition. The moving boundary condition which results is not solvable by similarity solutions, but can be solved by integral equation techniques. A solution process is outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic of a dissolving polymer

Triangular and Y-shaped hadrons with static sources

The structure of hadrons consisting of three static color sources in fundamental (baryons) or adjoint (three-gluon glueballs) representations is studied. The static potentials of glueballs as well as gluon field distributions in glueballs and baryons are calculated in the framework of field correlator method.Comment: 7 pages, 5 figures, talk at the NPD-2002 Conference, December 2-6, ITEP, Moscow, reference adde

The Evolution of Adiabatic Supernova Remnants in a Turbulent, Magnetized Medium

(Abridged) We present the results of three dimensional calculations for the MHD evolution of an adiabatic supernova remnant in both a uniform and turbulent interstellar medium using the RIEMANN framework of Balsara. In the uniform case, which contains an initially uniform magnetic field, the density structure of the shell remains largely spherical, while the magnetic pressure and synchrotron emissivity are enhanced along the plane perpendicular to the field direction. This produces a bilateral or barrel-type morphology in synchrotron emission for certain viewing angles. We then consider a case with a turbulent external medium as in Balsara & Pouquet, characterized by $v_{A}(rms)/c_{s}=2$. Several important changes are found. First, despite the presence of a uniform field, the overall synchrotron emissivity becomes approximately spherically symmetric, on the whole, but is extremely patchy and time-variable, with flickering on the order of a few computational time steps. We suggest that the time and spatial variability of emission in early phase SNR evolution provides information on the turbulent medium surrounding the remnant. The shock-turbulence interaction is also shown to be a strong source of helicity-generation and, therefore, has important consequences for magnetic field generation. We compare our calculations to the Sedov-phase evolution, and discuss how the emission characteristics of SNR may provide a diagnostic on the nature of turbulence in the pre-supernova environment.Comment: ApJ, in press, 5 color figure

A superspace formulation of an "asymptotic" OSp(3,1|2) invariance of Yang-Mills theories

We formulate a superspace field theory which is shown to be equivalent to the $c-\bar{c}$ symmetric BRS/Anti-BRS invariant Yang-Mills action. The theory uses a 6-dimensional superspace and one OSp(3,1|2) vector multiplet of unconstrained superfields. We establish a superspace WT identity and show that the formulation has an asymptotic OSp(3,1|2) invariance as the gauge parameter goes to infinity. We give a physical interpretation of this asymptotic OSp(3,1|2) invariance as a symmetry transformation among the longitudinal/time like degrees of freedom of $A_\mu$ and the ghost degrees of freedom.Comment: Latex, 20pages, No fig