33,726 research outputs found
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
Fractional Euler-Lagrange differential equations via Caputo derivatives
We review some recent results of the fractional variational calculus.
Necessary optimality conditions of Euler-Lagrange type for functionals with a
Lagrangian containing left and right Caputo derivatives are given. Several
problems are considered: with fixed or free boundary conditions, and in
presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will
appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu
et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in
pres
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
Temporal Analysis of Activity Patterns of Editors in Collaborative Mapping Project of OpenStreetMap
In the recent years Wikis have become an attractive platform for social
studies of the human behaviour. Containing millions records of edits across the
globe, collaborative systems such as Wikipedia have allowed researchers to gain
a better understanding of editors participation and their activity patterns.
However, contributions made to Geo-wikis_wiki-based collaborative mapping
projects_ differ from systems such as Wikipedia in a fundamental way due to
spatial dimension of the content that limits the contributors to a set of those
who posses local knowledge about a specific area and therefore cross-platform
studies and comparisons are required to build a comprehensive image of online
open collaboration phenomena. In this work, we study the temporal behavioural
pattern of OpenStreetMap editors, a successful example of geo-wiki, for two
European capital cities. We categorise different type of temporal patterns and
report on the historical trend within a period of 7 years of the project age.
We also draw a comparison with the previously observed editing activity
patterns of Wikipedia.Comment: Submitte
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
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