On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$. This result applies in particular to the algebra underlying inhomogeneous quantum groups like the Euclidean ones, which are obtained as cross-products of the quantum Euclidean spaces $R_q^N$ with the quantum groups of rotation $U_qso(N)$ of $R_q^N$, for which it has no classical analog.Comment: Latex file, 27 pages. Final version to appear in J. Phys.

Iron line emission in X-ray afterglows

Recent observations of X-ray afterglows reveal the presence of a redshifted Kalpha iron line in emission in four bursts. In GRB 991216, the line was detected by the low energy grating of Chandra, which showed the line to be broad, with a full width of ~15,000 km/s. These observations indicate the presence of a >1 solar mass of iron rich material in the close vicinity of the burst, most likely a supernova remnant. The fact that such strong lines are observed less than a day after the trigger strongly limits the size of the remnant, which must be very compact. If the remnant had the observed velocity since the supernova explosion, its age would be less than a month. In this case nickel and cobalt have not yet decayed into iron. We show how to solve this paradox.Comment: 3 pages, to appear in the proceedings of the the 2nd Workshop on Gamma-Ray Bursts in the Afterglow Era, Rome, Oct. 200

Analysis of X-ray flares in GRBs

We present a detailed study of the spectral and temporal properties of the X-ray flares emission of several GRBs. We select a sample of GRBs which X-ray light curve exhibits large amplitude variations with several rebrightenings superposed on the underlying three-segment broken powerlaw that is often seen in Swift GRBs. We try to understand the origin of these fluctuations giving some diagnostic in order to discriminate between refreshed shocks and late internal shocks. For some bursts our time-resolved spectral analysis supports the interpretation of a long-lived central engine, with rebrightenings consistent with energy injection in refreshed shocks as slower shells generated in the central engine prompt phase catch up with the afterglow shock at later times.Comment: 9 pages, 3 figures. Invited talk at the Swift-Venice 2006 meeting to be published by "Il Nuovo Cimento

Extinction properties of the X-ray bright/optically faint afterglow of GRB 020405

We present an optical-to-X-ray spectral analysis of the afterglow of GRB 020405. The optical spectral energy distribution not corrected for the extragalactic extinction is significantly below the X-ray extrapolation of the single powerlaw spectral model suggested by multiwavelength studies. We investigate whether considerable extinction could explain the observed spectral ``mismatch'' by testing several types of extinction curves. For the first time we test extinction curves computed with time-dependent numerical simulations of dust grains destruction by the burst radiation. We find that an extinction law weakly depen dent on wavelength can reconcile the unabsorbed optical and X-ray data with the expected synchrotron spectrum. A gray extinction law can be provided by a dust grain size distribution biased toward large grains.Comment: 6 pages, 5 figures, accepted for publication on A&

Deforming Maps for Lie Group Covariant Creation and Annihilation Operators

Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie algebra g and its deformation is induced by some triangular deformation $U_h g$ of the Hopf algebra $Ug$. We propose a systematic method to construct all the corresponding deforming maps, together with the corresponding realizations of the action of $U_h g$. The method is then generalized and explicitly applied to the case that $U_h g$ is the quantum group $U_h sl(2)$. A preliminary study of the status of deforming maps at the representation level shows in particular that `deformed' Fock representations induced by a compact $U_h g$ can be interpreted as standard `undeformed' Fock representations describing particles with ordinary Bose or Fermi statistics.Comment: Latex file, 26 pages, no figures. Extended changes. Final Version to appear in J. Math. Phy

Frame formalism for the N-dimensional quantum Euclidean spaces

We sketch our recent application of a non-commutative version of the Cartan `moving-frame' formalism to the quantum Euclidean space $R^N_q$, the space which is covariant under the action of the quantum group $SO_q(N)$. For each of the two covariant differential calculi over $R^N_q$ based on the $R$-matrix formalism, we summarize our construction of a frame, the dual inner derivations, a metric and two torsion-free almost metric compatible covariant derivatives with a vanishing curvature. To obtain these results we have developed a technique which fully exploits the quantum group covariance of $R^N_q$. We first find a frame in the larger algebra \Omega^*(R^N_q) \cocross \uqs. Then we define homomorphisms from R^N_q \cocross U_q^{\pm}{so(N)} to $R^N_q$ which we use to project this frame in $\Omega^*(R^N_q)$.Comment: Latex file, 11 pages. Talks given at the Euroconference ``Non-commutative Geometry and Hopf Algebras in Field Theory and Particle Physics'', Villa Gualino (Torino), Sept. 199

Extragalactic gamma-ray background from AGN winds and star-forming galaxies in cosmological galaxy formation models

We derive the contribution to the extragalactic gamma-ray background (EGB) from AGN winds and star-forming galaxies by including a physical model for the gamma-ray emission produced by relativistic protons accelerated by AGN-driven and supernova-driven shocks into a state-of-the-art semi-analytic model of galaxy formation. This is based on galaxy interactions as triggers of AGN accretion and starburst activity and on expanding blast wave as the mechanism to communicate outwards the energy injected into the interstellar medium by the active nucleus. We compare the model predictions with the latest measurement of the EGB spectrum performed by the Fermi-LAT in the range between 100 MeV and 820 GeV. We find that AGN winds can provide ~35$\pm$15% of the observed EGB in the energy interval E_{\gamma}=0.1-1 GeV, for ~73$\pm$15% at E_{\gamma}=1-10 GeV, and for ~60$\pm$20% at E_{\gamma}>10 GeV. The AGN wind contribution to the EGB is predicted to be larger by a factor of 3-5 than that provided by star-forming galaxies (quiescent plus starburst) in the hierarchical clustering scenario. The cumulative gamma-ray emission from AGN winds and blazars can account for the amplitude and spectral shape of the EGB, assuming the standard acceleration theory, and AGN wind parameters that agree with observations. We also compare the model prediction for the cumulative neutrino background from AGN winds with the most recent IceCube data. We find that for AGN winds with accelerated proton spectral index p=2.2-2.3, and taking into account internal absorption of gamma-rays, the Fermi-LAT and IceCube data could be reproduced simultaneously.Comment: 12 pages, 8 figures, accepted for publication in A&

q-Deformed quaternions and su(2) instantons

We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion language we have formulated and found solutions of the (anti)selfduality equation [instantons and multi-instantons] of a would-be deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on some noncommuting parameters, indicating that the moduli space of a complete theory should be a noncommutative manifold. We summarize these results and add an explicit comparison between the two SO_q(4)-covariant differential calculi on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi- (resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially coincide.Comment: Latex file, 18 page