11643138
CONFORMAL STRUCTURES AND TWISTORS IN THE PARAVECTOR MODEL OF SPACETIME
Some properties of the Clifford algebras and are presented, and three isomorphisms between the Dirac–Clifford algebra and are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU(2,2) and the group $pin+(2,4) is also investigated, in the light of a suitable isomorphism between and . After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $pin+(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian ℝ4,1 spacetime. We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac–Clifford algebra using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over ℝ4,1 is also used to describe conformal maps, instead of ℝ2,4. Our formalism sheds some new light on the use of the paravector model and generalizations.
118939700
Conformal Klein-Gordon Equations and Quasinormal Modes
Using conformal coordinates associated with conformal relativity—associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime—we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Pöschl-Teller potential, here we deduce and analytically solve a conformal ‘radial’ d’Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this ‘radial’ equation can be identified with a Schrödinger-like equation in which the potential is exactly the second Pöschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.
115165876
κ-DEFORMED POINCARÉ ALGEBRAS AND QUANTUM CLIFFORD–HOPF ALGEBRAS
The Minkowski space–time quantum Clifford algebra structure associated with the conformal group and the Clifford–Hopf alternative κ-deformed quantum Poincare algebra is investigated in the Atiyah–Bott–Shapiro mod 8 theorem context. The resulting algebra is equivalent to the deformed anti-de Sitter algebra , when the associated Clifford–Hopf algebra is taken into account, together with the associated quantum Clifford algebra and a (not braided) deformation of the periodicity Atiyah–Bott–Shapiro theorem.
118869110
Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.
118720958
Torsion Effects in Braneworld Scenarios
We present gravitational aspects of braneworld models endowed with torsion terms both in the bulk and on the brane. In order to investigate a conceivable and measurable gravitational effect, arising genuinely from bulk torsion terms, we analyze the variation in the black hole area by the presence of torsion. Furthermore, we extend the well-known results about consistency conditions in a framework that incorporates brane torsion terms. It is shown, in a rough estimate, that the resulting effects are generally suppressed by the internal space volume. This formalism provides manageable models and their possible ramifications into some aspects of gravity in this context, and cognizable corrections and physical effects as well.
115163234
ELKO, Flagpole and Flag-Dipole Spinor Fields, and the Instanton Hopf Fibration
Abstract.In a previous paper we explicitly constructed a mapping that leads Dirac spinor fields to the dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields). ELKO spinor fields are prime candidates for describing dark matter, and belong to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification, based on the relations and values taken by their associated bilinear covariants. Such a mapping between Dirac and ELKO spinor fields was obtained in an attempt to extend the Standard Model in order to encompass dark matter. Now we prove that such a mapping, analogous to the instanton Hopf fibration map S3...S7 → S4, indicates that ELKO is not suitable to describe the instanton. We review ELKO spinor fields as type-(5) spinor fields under the Lounesto spinor field classification, explicitly computing the associated bilinear covariants. This paper is also devoted to investigate some formal aspects of the flag-dipole spinor fields, which correspond to the class-(4) under the Lounesto spinor field classification and, in addition, we prove that type-(4) spinor fields — corresponding to flag-dipoles — and ELKO spinor fields — corresponding to flagpoles — can also be entirely described in terms of the Majorana and Weyl spinor fields. After all, by choosing a projection endomorphism of the spacetime algebra $${\mathcal C}\ell_{1,3}$$ it is shown how to obtain ELKO, flagpole, Majorana and Weyl spinor fields, respectively corresponding to type-(5) and -(6) spinor fields, uniquely from limiting cases of a type-(4) — flag-dipole — spinor field, in a similar result obtained by Lounesto.
62161359
Web enabled data management with DPM & LFC
The Disk Pool Manager (DPM) and LCG File Catalog (LFC) are two grid data management components currently used in production with more than 240 endpoints. Together with a set of grid client tools they give the users a unified view of their data, hiding most details concerning data location and access. Recently we've put a lot of effort in developing a reliable and high performance HTTP/WebDAV frontend to both our grid catalog and storage components, exposing the existing functionality to users accessing the services via standard clients - e.g. web browsers, curl - present in all operating systems, giving users a simple and straight-forward way of interaction. In addition, as other relevant grid storage components (like dCache) expose their data using the same protocol, for the first time we had the opportunity of attempting a unified view of all grid storage using HTTP. We describe the HTTP redirection mechanism used to integrate the grid catalog(s) with the multiple storage components, including details on some assumptions made to allow integration with other implementations. We describe the way we hide the details regarding site availability or catalog inconsistencies by switching the standard HTTP client automatically between multiple replicas. We also present measurements of access performance, and the relevant factors regarding replica selection - current throughput and load, geographic proximity, etc. Finally, we report on some additional work done to have this system as a viable alternative to GridFTP, providing multi-stream transfers and exploiting some additional features of WebDAV to enable third party copies - essential for managing data movements between storage systems - with equivalent performance.