Neutrinos and Electromagnetic Gauge Invariance

It is discussed a recently proposed connection among U(1)$_{\rm em}$ electromagnetic gauge invariance and the nature of the neutrino mass terms in the framework of \mbox {SU(3)}_C\otimes G_W \otimes {\mbox U(1)}_N, $G_W$ = SU(3)$_L$, extensions of the Standard Model. The impossibility of that connection, also in the extended case $G_W$ = SU(4)$_L$, is demonstrated.Comment: 10 pages, Revtex 3.0, no figure

A monopole solution from noncommutative multi-instantons

We extend the relation between instanton and monopole solutions of the selfduality equations in SU(2) gauge theory to noncommutative space-times. Using this approach and starting from a noncommutative multi-instanton solution we construct a U(2) monopole configuration which lives in 3 dimensional ordinary space. This configuration resembles the Wu-Yang monopole and satisfies the selfduality (Bogomol'nyi) equations for a U(2) Yang-Mills-Higgs system.Comment: 19 pages; title and abstract changed, brane interpretation corrected. Version to appear in JHE

Probing ferroelectricity in highly conducting materials through their elastic response: persistence of ferroelectricity in metallic BaTiO3-d

The question whether ferroelectricity (FE) may coexist with a metallic or highly conducting state, or rather it must be suppressed by the screening from the free charges, is the focus of a rapidly increasing number of theoretical studies and is finally receiving positive experimental responses. The issue is closely related to the thermoelectric and multiferroic (also magnetic) applications of FE materials, where the electrical conductivity is required or spurious. In these circumstances, the traditional methods for probing ferroelectricity are hampered or made totally ineffective by the free charges, which screen the polar response to an external electric field. This fact may explain why more than 40 years passed between the first proposals of FE metals and the present experimental and theoretical activity. The measurement of the elastic moduli, Young's modulus in the present case, versus temperature is an effective method for studying the influence of doping on a FE transition because the elastic properties are unaffected by electrical conductivity. In this manner, it is shown that the FE transitions of BaTiO3-d are not suppressed by electron doping through O vacancies; only the onset temperatures are depressed, but the magnitudes of the softenings, and hence of the piezoelectric activity, are initially even increased

Positive Ricci curvature through Cheeger deformation

Let $(M,g)$ be a Riemannian manifold with an isometric $G$-action. If a principal orbit has finite fundamental group and $\mathrm{Ric}_{M^{reg}/G}\geq 1$, Searle--Wilhelm proved that $M$ admits a new metric $\tilde g$ of positive Ricci curvature. $\tilde g$ is obtained after a conformal change followed by a Cheeger deformation. The question remained on whether it is sufficient to consider only the Cheeger deformation to attain positive Ricci curvature on the new metric $\tilde g$. Here we approach this question by giving necessary and sufficient conditions on the $G$-action. In particular, we construct an infinite family of manifolds satisfying the hypothesis of Searle--Wilhelm that do not develop positive Ricci curvature after Cheeger deformation. Further exploring the theory, we give a alternative proofs for Lawson--Yau result on positive scalar curvature under non-abelian symmetry, among others.Comment: 26 pages. Exposition reviewed. Applications include

Solar type II radio bursts associated with CME expansions as shown by EUV waves

We investigate the physical conditions of the sources of two metric Type-II bursts associated with CME expansions with the aim of verifying the relationship between the shocks and the CMEs, comparing the heights of the radio sources and the heights of the EUV waves associated with the CMEs. The heights of the EUV waves associated with the events were determined in relation to the wave fronts. The heights of the shocks were estimated by applying two different density models to the frequencies of the Type-II emissions and compared with the heights of the EUV waves. For the 13 June 2010 event, with band-splitting, the shock speed was estimated from the frequency drifts of the upper and lower branches of the harmonic lane, taking into account the H/F frequency ratio fH/fF = 2. Exponential fits on the intensity maxima of the branches revealed to be more consistent with the morphology of the spectrum of this event. For the 6 June 2012 event, with no band-splitting and with a clear fundamental lane on the spectrum, the shock speed was estimated directly from the frequency drift of the fundamental emission, determined by linear fit on the intensity maxima of the lane. For each event, the most appropriate density model was adopted to estimate the physical parameters of the radio source. The 13 June 2010 event presented a shock speed of 664-719 km/s, consistent with the average speed of the EUV wave fronts of 609 km/s. The 6 June 2012 event was related to a shock of speed of 211-461 km/s, also consistent with the average speed of the EUV wave fronts of 418 km/s. For both events, the heights of the EUV wave revealed to be compatible with the heights of the radio source, assuming a radial propagation of the shock.Comment: Accepted for publication in Astronomy and Astrophysic