33,791 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
The dust masses of powerful radio galaxies: clues to the triggering of their activity
We use deep Herschel Space Observatory observations of a 90% complete sample
of 32 intermediate-redshift 2Jy radio galaxies (0.05 < z < 0.7) to estimate the
dust masses of their host galaxies and thereby investigate the triggering
mechanisms for their quasar-like AGN. The dust masses derived for the radio
galaxies (7.2x10^5 < M_d < 2.6x10^8 M_sun) are intermediate between those of
quiescent elliptical galaxies on the one hand, and ultra luminous infrared
galaxies (ULIRGs) on the other. Consistent with simple models for the
co-evolution of supermassive black holes and their host galaxies, these results
suggest that most of the radio galaxies represent the late time re-triggering
of AGN activity via mergers between the host giant elliptical galaxies and
companion galaxies with relatively low gas masses. However, a minority of the
radio galaxies in our sample (~20%) have high, ULIRG-like dust masses, along
with evidence for prodigious star formation activity. The latter objects are
more likely to have been triggered in major, gas-rich mergers that represent a
rapid growth phase for both their host galaxies and their supermassive black
holes.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter
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 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 with the behaviour of the
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
BAHC.Comment: Version 4. 8 pages, 15 figures (12 figures in document
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