The hidden geometric character of relativistic quantum mechanics

The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in an hyperbolic space this fact leads inevitably to a wave equation with plane-like solutions. This is also true for 5-dimensional spacetime and we will explore those solutions, establishing a parallel with the solutions of the Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4x4 matrices, also known as Dirac's matrices. There is one problem with this isomorphism, because the solutions to Dirac's equation are usually known as spinors (column matrices) that don't belong to the 4x4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive/negative energy together with left/right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate 4-fold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.Comment: 29 pages. Small changes in V3 suggested by refere

DMRG study of the Bond Alternating \textbf{S}=1/2 Heisenberg ladder with Ferro-Antiferromagnetic couplings

We obtain the phase diagram in the parameter space $(J'/J, \gamma)$ and an accurate estimate of the critical line separating the different phases. We show several measuments of the magnetization, dimerization, nearest neighbours correlation, and density of energy in the different zones of the phase diagram, as well as a measurement of the string order parameter proposed as the non vanishing phase order parameter characterizing Haldane phases. All these results will be compared in the limit $J'/J\gg 1$ with the behaviour of the $\textbf{S}=1$ Bond Alternated Heisenberg Chain (BAHC). The analysis of our data supports the existence of a dimer phase separated by a critical line from a Haldane one, which has exactly the same nature as the Haldane phase in the $\textbf{S}=1$ BAHC.Comment: Version 4. 8 pages, 15 figures (12 figures in document

Microlensing path parametrization for Earth-like Exoplanet detection around solar mass stars

We propose a new parametrization of the impact parameter u0 and impact angle {\alpha} for microlensing systems composed by an Earth-like Exoplanet around a Solar mass Star at 1 AU. We present the caustic topology of such system, as well as the related light curves generated by using such a new parametrization. Based on the same density of points and accuracy of regular methods, we obtain results 5 times faster for discovering Earth-like exoplanet. In this big data revolution of photometric astronomy, our method will impact future missions like WFIRST (NASA) and Euclid (ESA) and they data pipelines, providing a rapid and deep detection of exoplanets for this specific class of microlensing event that might otherwise be lost.Comment: 8 pages, 7 figures, accepted to be published in The Astronomical Journa

The radiation of a uniformly accelerated charge is beyond the horizon: a simple derivation

We show, by exploring some elementary consequences of the covariance of Maxwell's equations under general coordinate transformations, that, despite inertial observers can indeed detect electromagnetic radiation emitted from a uniformly accelerated charge, comoving observers will see only a static electric field. This simple analysis can help understanding one of the most celebrated paradoxes of last century.Comment: Revtex, 6 pages, 2 figures. v2: Some small corrections. v3: Citation of a earlier paper included. v4: Some stylistic changes. v5: Final version to appear in AJ

Testing the Equivalence of Regular Languages

The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algorithm to non-deterministic finite automata, and establish a relationship between this algorithm and the one proposed in Almeida et al. We also present some experimental comparative results. All these algorithms are closely related with the recent coalgebraic approach to automata proposed by Rutten

Polarization of the changing-look quasar J1011+5442

If the disappearance of the broad emission lines observed in changing-look quasars were caused by the obscuration of the quasar core through moving dust clouds in the torus, high linear polarization typical of type 2 quasars would be expected. We measured the polarization of the changing-look quasar J1011+5442 in which the broad emission lines have disappeared between 2003 and 2015. We found a polarization degree compatible with null polarization. This measurement suggests that the observed change of look is not due to a change of obscuration hiding the continuum source and the broad line region, and that the quasar is seen close to the system axis. Our results thus support the idea that the vanishing of the broad emission lines in J1011+5442 is due to an intrinsic dimming of the ionizing continuum source that is most likely caused by a rapid decrease in the rate of accretion onto the supermassive black hole.Comment: Accepted for publication in Astronomy and Astrophysics Letter