The Mass Spectrum of Neutrinos

In a previous paper we showed that Weyl equation possess superluminal solutions and moreover we showed that those solutions that are eigenstates of the parity operator seem to describe a coupled pair of a monopole anti-monopole system. This result suggests to look for a solution of Maxwell equation \partialF^{\infty}=-gJ with a current J as source and such that the Lorentz force on the current is null. We first identify a solution where J={\gamma}^{5}J_{m}is a spacelike field (even if F is not a superluminal solution of the homogeneous Maxwell equation). More surprisingly we find that there exists a solution F of the free Maxwell \partialF=0 that is equivalent to the non homogeneous equation for F^{\infty}. Once this result is proved it suggests by itself to look for more general subluminal and superluminal solutions F of the free Maxwell equation equivalent to a non homogeneous Maxwell equation for a field F_{0} with a current term as source which may be subluminal or superluminal. We exhibit one such subluminal solution, for which the Dirac-Hestenes spinor field {\psi} associated the electromagnetic field F_{0} satisfies a Dirac equation for a bradyonic neutrino under the ansatz that the current is ce^{{\lambda}{\gamma}^{5}}g{\psi}{\gamma}^{0}{\psi}, with g the quantum of magnetic charge and {\lambda} a constant to be determined in such a way that the auto-force be null. Together with Dirac's quantization condition this gives a quantized mass spectrum (Eq.49) for the neutrinos, with the masses of the different flavor neutrinos being of the same order of magnitude (Eq.50) which is in accord with recent experimental findings. As a last surprise we show that the mass spectrum found in the previous case continues to hold if the current is taken spacelike, i.e., ce^{{\lambda}{\gamma}^{5}}g{\psi}_{>}{\gamma}^{3}{\psi}_{>} with {\psi}_{>}, in this case, satisfying a tachyonic Dirac-Hestenes equation.Comment: This version corrects some misprints, has a new remark and a new referenc

Searching High Redshift Large-Scale Structures: Photometry of Four Fields Around Quasar Pairs at z~1

We have studied the photometric properties of four fields around the high-redshift quasar pairs QP1310+0007, QP1355-0032, QP0110-0219, and QP0114-3140 at z ~ 1 with the aim of identifying large-scale structures- galaxy clusters or groups- around them. This sample was observed with GMOS in Gemini North and South telescopes in the g', r', i', and z' bands, and our photometry is complete to a limiting magnitude of i' ~ 24 mag (corresponding to ~ M*_i' + 2 at the redshift of the pairs). Our analysis reveals that QP0110-0219 shows very strong and QP1310+0007 and QP1355-0032 show some evidence for the presence of rich galaxy clusters in direct vicinity of the pairs. On the other hand, QP0114-3140 could be an isolated pair in a poor environment. This work suggest that z ~ 1 quasar pairs are excellent tracers of high density environments and this same technique may be useful to find clusters at higher redshifts.Comment: 29 pages, 7 figures, ApJ accepted. Added one figure and 3 references. Some paragraphs was rewritten in sections 1, 3, 5, and 6, as suggested by refere

Can the evolution of music be analyzed in a quantitative manner?

We propose a methodology to study music development by applying multivariate statistics on composers characteristics. Seven representative composers were considered in terms of eight main musical features. Grades were assigned to each characteristic and their correlations were analyzed. A bootstrap method was applied to simulate hundreds of artificial composers influenced by the seven representatives chosen. Afterwards we quantify non-numeric relations like dialectics, opposition and innovation. Composers differences on style and technique were represented as geometrical distances in the feature space, making it possible to quantify, for example, how much Bach and Stockhausen differ from other composers or how much Beethoven influenced Brahms. In addition, we compared the results with a prior investigation on philosophy. Opposition, strong on philosophy, was not remarkable on music. Supporting an observation already considered by music theorists, strong influences were identified between composers by the quantification of dialectics, implying inheritance and suggesting a stronger master-disciple evolution when compared to the philosophy analysis.Comment: 8 pages, 6 figures, added references for sections 1 and 4.C, better mathematical description on section 2. New values and interpretation, now considering a bootstrap metho

Gauging N=2 Supersymmetric Non-Linear σ\sigma-Models in the Atiyah-Ward Space-Time

We build up a class of N=2 supersymmetric non-linear $\sigma$-models in an N=1 superspace based on the Atiyah-Ward space-time of (2+2)-signature metric. We also discuss the gauging of isometries of the associated hyper-K\"ahlerian target spaces and present the resulting gauge-covariant supersymmetric action functional.Comment: 12 pages, latex, no figure