Optical-inertia space sextant for an advanced space navigation system, phase B

Optical-inertia space sextant for advanced space navigation syste

Primary Particle Type of the Most Energetic Fly's Eye Air Shower

The longitudinal profile of the most energetic cosmic-ray air shower measured so far, the event recorded by the Fly's Eye detector with a reconstructed primary energy of about 320 EeV, is compared to simulated shower profiles. The calculations are performed with the CORSIKA code and include primary photons and different hadron primaries. For primary photons, preshower formation in the geomagnetic field is additionally treated in detail. For primary hadrons, the hadronic interaction models QGSJET01 and SIBYLL2.1 have been employed. The predicted longitudinal profiles are compared to the observation. A method for testing the hypothesis of a specific primary particle type against the measured profile is described which naturally takes shower fluctuations into account. The Fly's Eye event is compatible with any assumption of a hadron primary between proton and iron nuclei in both interaction models, although differences between QGSJET01 and SIBYLL2.1 in the predicted profiles of lighter nuclei exist. The primary photon profiles differ from the data on a level of ~1.5 sigma. Although not favoured by the observation, the primary photon hypothesis can not be rejected for this particular event.Comment: 20 pages, 8 figures; v2 matches version accepted by Astroparticle Physic

Large Chiral Diffeomorphisms on Riemann Surfaces and W-algebras

The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a B.R.S. formulation (for a given order of truncation) leading to a more algebraic set up. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between KdV flows and W-diffeomorphimsComment: LaTeX file, 31 pages, no figure. Version to appear in J. Math. Phys. Work partly supported by Region PACA and INF

Symmetries of modules of differential operators

Let ${\cal F}\_\lambda(S^1)$ be the space of tensor densities of degree (or weight) $\lambda$ on the circle $S^1$. The space ${\cal D}^k\_{\lambda,\mu}(S^1)$ of $k$-th order linear differential operators from ${\cal F}\_\lambda(S^1)$ to ${\cal F}\_\mu(S^1)$ is a natural module over $\mathrm{Diff}(S^1)$, the diffeomorphism group of $S^1$. We determine the algebra of symmetries of the modules ${\cal D}^k\_{\lambda,\mu}(S^1)$, i.e., the linear maps on ${\cal D}^k\_{\lambda,\mu}(S^1)$ commuting with the $\mathrm{Diff}(S^1)$-action. We also solve the same problem in the case of straight line $\mathbb{R}$ (instead of $S^1$) and compare the results in the compact and non-compact cases.Comment: 29 pages, LaTeX, 4 figure