The Eastwood-Singer gauge in Einstein spaces

Electrodynamics in curved spacetime can be studied in the Eastwood--Singer gauge, which has the advantage of respecting the invariance under conformal rescalings of the Maxwell equations. Such a construction is here studied in Einstein spaces, for which the Ricci tensor is proportional to the metric. The classical field equations for the potential are then equivalent to first solving a scalar wave equation with cosmological constant, and then solving a vector wave equation where the inhomogeneous term is obtained from the gradient of the solution of the scalar wave equation. The Eastwood--Singer condition leads to a field equation on the potential which is preserved under gauge transformations provided that the scalar function therein obeys a fourth-order equation where the highest-order term is the wave operator composed with itself. The second-order scalar equation is here solved in de Sitter spacetime, and also the fourth-order equation in a particular case, and these solutions are found to admit an exponential decay at large time provided that square-integrability for positive time is required. Last, the vector wave equation in the Eastwood-Singer gauge is solved explicitly when the potential is taken to depend only on the time variable.Comment: 13 pages. Section 6, with new original calculations, has been added, and the presentation has been improve

Using Gravitational Lensing to study HI clouds at high redshift

We investigate the possibility of detecting HI emission from gravitationally lensed HI clouds (akin to damped Lyman-$\alpha$ clouds) at high redshift by carrying out deep radio observations in the fields of known cluster lenses. Such observations will be possible with present radio telescopes only if the lens substantially magnifies the flux of the HI emission. While at present this holds the only possibility of detecting the HI emission from such clouds, it has the disadvantage of being restricted to clouds that lie very close to the caustics of the lens. We find that observations at a detection threshold of 50 micro Jy at 320 MHz (possible with the GMRT) have a greater than 20% probability of detecting an HI cloud in the field of a cluster, provided the clouds have HI masses in the range 5 X 10^8 M_{\odot} < M_{HI} < 2.5 X 10^{10} M_{\odot}. The probability of detecting a cloud increases if they have larger HI masses, except in the cases where the number of HI clouds in the cluster field becomes very small. The probability of a detection at 610 MHz and 233 MHz is comparable to that at 320 MHz, though a definitive statement is difficult owing to uncertainties in the HI content at the redshifts corresponding to these frequencies. Observations at a detection threshold of 2 micro Jy (possible in the future with the SKA) are expected to detect a few HI clouds in the field of every cluster provided the clouds have HI masses in the range 2 X 10^7 M_{\odot} < M_{HI} < 10^9 M_{\odot}. Even if such observations do not result in the detection of HI clouds, they will be able to put useful constraints on the HI content of the clouds.Comment: 21 pages, 7 figures, minor changes in figures, accepted for publication in Ap

Seeking the Ultraviolet Ionizing Background at z~3 with the Keck Telescope

We describe the initial results of a deep long-slit emission line search for redshifted (2.7<z<4.1) Lyman-alpha. These observations are used to constrain the fluorescent Ly-alpha emission from the population of clouds whose absorption produces the higher-column-density component of the Ly-alpha forest in quasar spectra. We use the results to set an upper limit on the ultraviolet ionizing background. Our spectroscopic data obtained with the Keck II telescope at lambda/(Delta lambda FWHM)~2000 reveals no candidate Ly-alpha emission over the wavelength range of 4500-6200 Ang along a 3 arcmin slit in a 5400 s integration. Our 3 sigma upper bound on the mean intensity of the ionizing background at the Lyman limit is J(nu 0) < 2E-21 erg/s/cm**2/Hz/sr for 2.7<z<3.1 (where we are most sensitive), assuming Lyman limit systems have typical radii of 70 kpc (q_0=0.5, H_0=50 km/s/Mpc). This constraint is more than an order of magnitude more stringent than any previously published direct limit. However, it is still a factor of three above the ultraviolet background level expected due to the integrated light of known quasars at z~3. This pilot study confirms the conclusion of Gould \& Weinberg (1996) that integrations of several hours on a 10-m class telescope should be capable of measuring J(nu 0) at high redshift.Comment: 22 pages, 2 postscipt figures. Latex requires aaspp4.sty and epsf.sty (included). Accepted for publication in the Astronomical Journal (Nov 1998

The Properties of Field Elliptical Galaxies at Intermediate Redshift. I: Empirical Scaling Laws

We present measurements of the Fundamental Plane (FP) parameters (the effective radius, the mean effective surface brightness, and the central velocity dispersion) of six field elliptical galaxies at intermediate redshift. The imaging is taken from the Medium Deep Survey of the Hubble Space Telescope, while the kinematical data are obtained from long-slit spectroscopy using the 3.6-m ESO telescope. The Fundamental Plane appears well defined in the field even at redshift $\approx$ 0.3. The data show a shift in the FP zero point with respect to the local relation, possibly indicating modest evolution, consistent with the result found for intermediate redshift cluster samples. The FP slopes derived for our field data, plus other cluster ellipticals at intermediate redshift taken from the literature, differ from the local ones, but are still consistent with the interpretation of the FP as a result of homology, of the virial theorem and of the existence of a relation between luminosity and mass, $L \propto M^{\eta}$. We also derive the surface brightness vs. effective radius relation for nine galaxies with redshift up to $z \approx0.6$, and data from the literature; the evolution that can be inferred is consistent with what is found using the FP.Comment: 17 pages, including 9 figures, MNRAS, accepte

Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron

Simulation of gauge transformations on systems of ultracold atoms

We show that gauge transformations can be simulated on systems of ultracold atoms. We discuss observables that are invariant under these gauge transformations and compute them using a tensor network ansatz that escapes the phase problem. We determine that the Mott-insulator-to-superfluid critical point is monotonically shifted as the induced magnetic flux increases. This result is stable against the inclusion of a small amount of entanglement in the variational ansatz.Comment: 14 pages, 6 figure

NICMOS Imaging of a Damped Lyman-alpha Absorber at z=1.89 toward LBQS 1210+1731 : Constraints on Size and Star Formation Rate

We report results of a high-resolution imaging search (in rest frame H-$\alpha$ and optical continuum) for the galaxy associated with the damped Lyman-$\alpha$ (DLA) absorber at $z=1.892$ toward the $z_{em}=2.543$ quasar LBQS 1210+1731, using HST/NICMOS. After PSF subtraction, a feature is seen in both the broad-band and narrow-band images, at a projected separation of 0.25\arcsec from the quasar. If associated with the DLA, the object would be $\approx 2-3$ $h_{70}^{-1}$ kpc in size with a flux of $9.8 \pm 2.4$ $\mu$Jy in the F160W filter, implying a luminosity at $\lambda_{central}=5500$ {\AA} in the rest frame of $1.5 \times 10^{10}$ $h_{70}^{-2}$ L$_{\odot}$ at $z=1.89$, for $q_{0}=0.5$. However, no significant H-$\alpha$ emission is seen, suggesting a low star formation rate (SFR) (3 $\sigma$ upper limit of 4.0 $h_{70}^{-2}$ M$_{\odot}$ yr$^{-1}$), or very high dust obscuration. Alternatively, the object may be associated with the host galaxy of the quasar. H-band images obtained with the NICMOS camera 2 coronagraph show a much fainter structure $\approx 4-5$ $h_{70}^{-1}$ kpc in size and containing four knots of continuum emission, located 0.7\arcsec away from the quasar. We have probed regions far closer to the quasar sight-line than in most previous studies of high-redshift intervening DLAs. The two objects we report mark the closest detected high-redshift DLA candidates yet to any quasar sight line. If the features in our images are associated with the DLA, they suggest faint, compact, somewhat clumpy objects rather than large, well-formed proto-galactic disks or spheroids.Comment: 52 pages of text, 19 figures, To be published in Astrophysical Journal (accepted Dec. 8, 1999

Rotating light, OAM paradox and relativistic complex scalar field

Recent studies show that the angular momentum, both spin and orbital, of rotating light beams possesses counter-intuitive characteristics. We present a new approach to the question of orbital angular momentum of light based on the complex massless scalar field representation of light. The covariant equation for the scalar field is treated in rotating system using the general relativistic framework. First we show the equivalence of the U(1) gauge current for the scalar field with the Poynting vector continuity equation for paraxial light, and then apply the formalism to the calculation of the orbital angular momentum of rotating light beams. If the difference between the co-, contra-, and physical quantities is properly accounted for there does not result any paradox in the orbital angular momentum of rotating light. An artificial analogue of the paradoxical situation could be constructed but it is wrong within the present formalism. It is shown that the orbital angular momentum of rotating beam comprising of modes with opposite azimuthal indices corresponds to that of rigid rotation. A short review on the electromagnetism in noninertial systems is presented to motivate a fully covariant Maxwell field approach in rotating system to address the rotating light phenomenon.Comment: No figure