Twisting commutative algebraic groups

If $V$ is a commutative algebraic group over a field $k$, $O$ is a commutative ring that acts on $V$, and $I$ is a finitely generated free $O$-module with a right action of the absolute Galois group of $k$, then there is a commutative algebraic group $I \otimes_O V$ over $k$, which is a twist of a power of $V$. These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori over finite fields) and to the arithmetic of abelian varieties over number fields. For purposes of such applications we devote this article to making explicit this tensor product construction and its basic properties.Comment: To appear in Journal of Algebra. Minor changes from original versio

Comparison of FDMA and CDMA for second generation land-mobile satellite communications

Code Division Multiple Access (CDMA) and Frequency Division Multiple Access (FDMA) (both analog and digital) systems capacities are compared on the basis of identical link availabilities and physical propagation models. Parameters are optimized for a bandwidth limited, multibeam environment. For CDMA, the benefits of voice activated carriers, antenna discrimination, polarization reuse, return link power control and multipath suppression are included in the analysis. For FDMA, the advantages of bandwidth efficient modulation/coding combinations, voice activated carriers, polarization reuse, beam placement, and frequency staggering were taken into account

Eclipsing Binaries in the OGLE Variable Star Catalog.III. Long-Period Contact Systems

A sample of contact binaries discovered by the OGLE project in Baade's Window, with orbital periods longer than one day and with available color and light-curve data, has been analyzed. It consists of only 32 systems, in contrast to 388 WUMa-type systems with shorter periods which were analyzed before. Most systems are very distant and are probably located close to or in the galactic Bulge. Two groups of contact binaries are seen in the sample: (1) a continuation of the WUMa-type sequence, extending up to the orbital periods of 1.3 - 1.5 day, but rather sharply ending in this period range; (2) an inhomogeneous group of rare systems with long periods up to 26 days, all with red colors and relatively shallow eclipses. While the systems of the first group share most of the characteristics of the typical WUMa-type systems (except that they are on the average brighter and more distant, hence more reddened), the long-period systems do not seem to form an early-type extension of contact binaries, but may consist of a mixture of late-type objects, including tidally distorted red giants with invisible companions.Comment: 24 pages including 10 figures (inserted with psfig) and one table; submitted to A

BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)

We consider the massless scalar field on the four-dimensional sphere $S^4$. Its classical action $S={1\over 2}\int_{S^4} dV (\nabla \phi)^2$ is degenerate under the global invariance $\phi \to \phi + \hbox{constant}$. We then quantize the massless scalar field as a gauge theory by constructing a BRST-invariant quantum action. The corresponding gauge-breaking term is a non-local one of the form $S^{\rm GB}={1\over {2\alpha V}}\bigl(\int_{S^4} dV \phi \bigr)^2$ where $\alpha$ is a gauge parameter and $V$ is the volume of $S^4$. It allows us to correctly treat the zero mode problem. The quantum theory is invariant under SO(5), the symmetry group of $S^4$, and the associated two-point functions have no infrared divergence. The well-known infrared divergence which appears by taking the massless limit of the massive scalar field propagator is therefore a gauge artifact. By contrast, the massless scalar field theory on de Sitter space $dS^4$ - the lorentzian version of $S^4$ - is not invariant under the symmetry group of that spacetime SO(1,4). Here, the infrared divergence is real. Therefore, the massless scalar quantum field theories on $S^4$ and $dS^4$ cannot be linked by analytic continuation. In this case, because of zero modes, the euclidean approach to quantum field theory does not work. Similar considerations also apply to massive scalar field theories for exceptional values of the mass parameter (corresponding to the discrete series of the de Sitter group).Comment: This paper has been published under the title "Zero modes, euclideanization and quantization" [Phys. Rev. D46, 2553 (1992)

Cosmological Dark Energy: Prospects for a Dynamical Theory

We present an approach to the problem of vacuum energy in cosmology, based on dynamical screening of Lambda on the horizon scale. We review first the physical basis of vacuum energy as a phenomenon connected with macroscopic boundary conditions, and the origin of the idea of its screening by particle creation and vacuum polarization effects. We discuss next the relevance of the quantum trace anomaly to this issue. The trace anomaly implies additional terms in the low energy effective theory of gravity, which amounts to a non-trivial modification of the classical Einstein theory, fully consistent with the Equivalence Principle. We show that the new dynamical degrees of freedom the anomaly contains provide a natural mechanism for relaxing Lambda to zero on cosmological scales. We consider possible signatures of the restoration of conformal invariance predicted by the fluctuations of these new scalar degrees of freedom on the spectrum and statistics of the CMB, in light of the latest bounds from WMAP. Finally we assess the prospects for a new cosmological model in which the dark energy adjusts itself dynamically to the cosmological horizon boundary, and therefore remains naturally of order H^2 at all times without fine tuning.Comment: 50 pages, Invited Contribution to New Journal of Physics Focus Issue on Dark Energ

Update on Radiation Dose From Galactic and Solar Protons at the Moon Using the LRO/CRaTER Microdosimeter

The NASA Lunar Reconnaissance Orbiter (LRO) has been exploring the lunar surface and radiation environment since June 2009. In Mazur et al. [2011] we discussed the first 6 months of mission data from a microdosimeter that is housed within the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) instrument onboard LRO. The CRaTER microdosimeter is an early version of what is now a commercially available hybrid that accurately measures total ionizing radiation dose in a silicon target (http://www.teledynemicro.com/product/radiation-dosimeter). This brief report updates the transition from a deep solar minimum radiation environment to the current weak solar maximum as witnessed with the microdosimeter

Large-scale radio continuum properties of 19 Virgo cluster galaxies The influence of tidal interactions, ram pressure stripping, and accreting gas envelopes

Deep scaled array VLA 20 and 6cm observations including polarization of 19 Virgo spirals are presented. This sample contains 6 galaxies with a global minimum of 20cm polarized emission at the receding side of the galactic disk and quadrupolar type large-scale magnetic fields. In the new sample no additional case of a ram-pressure stripped spiral galaxy with an asymmetric ridge of polarized radio continuum emission was found. In the absence of a close companion, a truncated HI disk, together with a ridge of polarized radio continuum emission at the outer edge of the HI disk, is a signpost of ram pressure stripping. 6 out of the 19 observed galaxies display asymmetric 6cm polarized emission distributions. Three galaxies belong to tidally interacting pairs, two galaxies host huge accreting HI envelopes, and one galaxy had a recent minor merger. Tidal interactions and accreting gas envelopes can lead to compression and shear motions which enhance the polarized radio continuum emission. In addition, galaxies with low average star formation rate per unit area have a low average degree of polarization. Shear or compression motions can enhance the degree of polarization. The average degree of polarization of tidally interacting galaxies is generally lower than expected for a given rotation velocity and star formation activity. This low average degree of polarization is at least partly due to the absence of polarized emission from the thin disk. Ram pressure stripping can decrease whereas tidal interactions most frequently decreases the average degree of polarization of Virgo spiral galaxies. We found that moderate active ram pressure stripping has no influence on the spectral index, but enhances the global radio continuum emission with respect to the FIR emission, while an accreting gas envelope can but not necessarily enhances the radio continuum emission with respect to the FIR emission.Comment: 37 pages, 26 figures, accepted for publication in A&

Quantum Diffeomorphisms and Conformal Symmetry

We analyze the constraints of general coordinate invariance for quantum theories possessing conformal symmetry in four dimensions. The character of these constraints simplifies enormously on the Einstein universe $R \times S^3$. The $SO(4,2)$ global conformal symmetry algebra of this space determines uniquely a finite shift in the Hamiltonian constraint from its classical value. In other words, the global Wheeler-De Witt equation is {\it modified} at the quantum level in a well-defined way in this case. We argue that the higher moments of $T^{00}$ should not be imposed on the physical states {\it a priori} either, but only the weaker condition $\langle \dot T^{00} \rangle = 0$. We present an explicit example of the quantization and diffeomorphism constraints on $R \times S^3$ for a free conformal scalar field.Comment: PlainTeX File, 37 page

Characteristic Energy of the Coulomb Interactions and the Pileup of States

Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the density of states. Importantly, the data and analysis at high energy, E, show a pileup of states: most of the states removed from near the Fermi level are found between ~40 and 130 meV, from which we infer the possibility of universal behavior. The agreement of our tunneling data with recent photoemission results further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR