Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

More Evidence for an Oscillation Superimposed on the Hubble Flow

In a recent investigation evidence was presented for a low-level sinusoidal oscillation superimposed on top of the Hubble flow. This oscillation was in V$_{CMB}$, in a sample of type Ia Supernovae sources with accurate distances, and it was found to have a wavelength close to 40 Mpc. It became easily visible after the removal of several previously identified discrete velocity components. Its amplitude like that of the Hubble velocity showed an increase with distance, as would be expected for a constant-amplitude space oscillation. Here we report that this oscillation is also present in distance clumping in these sources, with the same wavelength, but in phase quadrature. The discrete velocity components do not play a role in detecting the distance clumping wavelength. Assuming that time proceeds from high cosmological redshift to low, the blue-shifted velocity peaks, which represent the contraction stage of the velocity oscillation, then lead the density peaks. With the discrete velocity components removed we also find evidence for at least one other, weaker velocity oscillation. It is found to have a wavelength similar to one reported in density clumping by previous investigators. In those cases the source samples were much larger.Comment: 7 pages, with 6 figures, accepted for publication in Astrophysics and Space Scienc

On The Depolarization Asymmetry Seen in Giant Radio Lobes

The depolarization asymmetry seen in double-lobed radio sources, referred to as the Laing-Garrington (L-G) effect where more rapid depolarization is seen in the lobe with no visible jet as the wavelength increases, can be explained either by internal differences between the two lobes, or by an external Faraday screen that lies in front of only the depolarized lobe. If the jet one-sidedness is due to relativistic beaming the depolarization asymmetry must be due to an intervening Faraday screen. If it is intrinsic the depolarization asymmetry must be related to internal differences in the lobes. We assume in this paper that the speed in the outer jet of several Fanaroff-Riley Class 1 (FRI) sources exhibiting the L-G effect is close to the 0.1c reported by several other investigators. For these sources we find that the jet one-sidedness cannot be explained by beaming and therefore must be intrinsic. In these FRI sources the L-G effect must be due to differences that originate inside the lobes themselves. Although it is not known if the flow in the outer jets of FRII sources also slows to this speed it is suggested that the explanation of the L-G effect is likely to be the same in both types. This argument is strengthened by the recent evidence that FRII galaxies have very large viewing angles, which in turn implies that the L-G model cannot work regardless of the jet velocity. It may therefore be too soon to completely rule out internal depolarization in the lobes as the true explanation for the L-G effect.Comment: 8 pages with 4 figures. Accepted for publication in Ap&S

WZW action in odd dimensional gauge theories

It is shown that Wess-Zumino-Witten (WZW) type actions can be constructed in odd dimensional space-times using Wilson line or Wilson loop. WZW action constructed using Wilson line gives anomalous gauge variations and the WZW action constructed using Wilson loop gives anomalous chiral transformation. We show that pure gauge theory including Yang-Mills action, Chern-Simons action and the WZW action can be defined in odd dimensional space-times with even dimensional boundaries. Examples in 3D and 5D are given. We emphasize that this offers a way to generalize gauge theory in odd dimensions. The WZW action constructed using Wilson line can not be considered as action localized on boundary space-times since it can give anomalous gauge transformations on separated boundaries. We try to show that such WZW action can be obtained in the effective theory when making localized chiral fermions decouple.Comment: 19 pages, text shortened, reference added. Version to appear in PR

The Relativistically Spinning Charged Sphere

When the equatorial spin velocity, $v$, of a charged conducting sphere approaches $c$, the Lorentz force causes a remarkable rearrangement of the total charge $q$. Charge of that sign is confined to a narrow equatorial belt at latitudes $b \leqslant \sqrt{3} (1 - v^2/c^2)^{{1/2}}$ while charge of the opposite sign occupies most of the sphere's surface. The change in field structure is shown to be a growing contribution of the `magic' electromagnetic field of the charged Kerr-Newman black hole with Newton's G set to zero. The total charge within the narrow equatorial belt grows as $(1-v^2/c^2)^{-{1/4}}$ and tends to infinity as $v$ approaches $c$. The electromagnetic field, Poynting vector, field angular momentum and field energy are calculated for these configurations. Gyromagnetic ratio, g-factor and electromagnetic mass are illustrated in terms of a 19th Century electron model. Classical models with no spin had the small classical electron radius $e^2/mc^2\sim$ a hundredth of the Compton wavelength, but models with spin take that larger size but are so relativistically concentrated to the equator that most of their mass is electromagnetic. The method of images at inverse points of the sphere is shown to extend to charges at points with imaginary co-ordinates.Comment: 15 pages, 1figur

An improved Riemann Mapping Theorem and complexity in potential theory

We discuss applications of an improvement on the Riemann mapping theorem which replaces the unit disc by another "double quadrature domain," i.e., a domain that is a quadrature domain with respect to both area and boundary arc length measure. Unlike the classic Riemann Mapping Theorem, the improved theorem allows the original domain to be finitely connected, and if the original domain has nice boundary, the biholomorphic map can be taken to be close to the identity, and consequently, the double quadrature domain close to the original domain. We explore some of the parallels between this new theorem and the classic theorem, and some of the similarities between the unit disc and the double quadrature domains that arise here. The new results shed light on the complexity of many of the objects of potential theory in multiply connected domains.Comment: 23 page

Causality and Cirel'son bounds

An EPR-Bell type experiment carried out on an entangled quantum system can produce correlations stronger than allowed by local realistic theories. However there are correlations that are no-signaling and are more non local than the quantum correlations. Here we show that any correlations more non local than those achievable in an EPR-Bell type experiment necessarily allow -in the context of the quantum formalism- both for signaling and for generation of entanglement. We use our approach to rederive Cirel'son bound for the CHSH expression, and we derive a new Cirel'son type bound for qutrits. We discuss in detail the interpretation of our approach.Comment: 5 page

How much larger quantum correlations are than classical ones

Considering as distance between two two-party correlations the minimum number of half local results one party must toggle in order to turn one correlation into the other, we show that the volume of the set of physically obtainable correlations in the Einstein-Podolsky-Rosen-Bell scenario is (3 pi/8)^2 = 1.388 larger than the volume of the set of correlations obtainable in local deterministic or probabilistic hidden-variable theories, but is only 3 pi^2/32 = 0.925 of the volume allowed by arbitrary causal (i.e., no-signaling) theories.Comment: REVTeX4, 6 page