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

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

Distinct magnetic signatures of fractional vortex configurations in multiband superconductors

Vortices carrying fractions of a flux quantum are predicted to exist in multiband superconductors, where vortex core can split between multiple band-specific components of the superconducting condensate. Using the two-component Ginzburg-Landau model, we examine such vortex configurations in a two-band superconducting slab in parallel magnetic field. The fractional vortices appear due to the band-selective vortex penetration caused by different thresholds for vortex entry within each band-condensate, and stabilize near the edges of the sample. We show that the resulting fractional vortex configurations leave distinct fingerprints in the static measurements of the magnetization, as well as in ac dynamic measurements of the magnetic susceptibility, both of which can be readily used for the detection of these fascinating vortex states in several existing multiband superconductors.Comment: 5 pages, 4 figure

Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space

We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the \delta-function singularity coming from the Zeeman spin interaction with the magnetic flux tube is solved through the self-adjoint extension method. Using two different approaches already known in the literature, both based on the self-adjoint extension method, we obtain the self-adjoint extension parameter to the bound state and scattering scenarios in terms of the physics of the problem. It is shown that such a parameter is the same for both situations. The method is general and is suitable for any quantum system with a singular Hamiltonian that has bound and scattering states.Comment: Revtex4, 5 pages, published versio

Strong evidences for a nonextensive behavior of the rotation period in Open Clusters

Time-dependent nonextensivity in a stellar astrophysical scenario combines nonextensive entropic indices $q_{K}$ derived from the modified Kawaler's parametrization, and $q$, obtained from rotational velocity distribution. These $q$'s are related through a heuristic single relation given by $q\approx q_{0}(1-\Delta t/q_{K})$, where $t$ is the cluster age. In a nonextensive scenario, these indices are quantities that measure the degree of nonextensivity present in the system. Recent studies reveal that the index $q$ is correlated to the formation rate of high-energy tails present in the distribution of rotation velocity. On the other hand, the index $q_{K}$ is determined by the stellar rotation-age relationship. This depends on the magnetic field configuration through the expression $q_{K}=1+4aN/3$, where $a$ and $N$ denote the saturation level of the star magnetic field and its topology, respectively. In the present study, we show that the connection $q-q_{K}$ is also consistent with 548 rotation period data for single main-sequence stars in 11 Open Clusters aged less than 1 Gyr. The value of $q_{K}\sim$ 2.5 from our unsaturated model shows that the mean magnetic field topology of these stars is slightly more complex than a purely radial field. Our results also suggest that stellar rotational braking behavior affects the degree of anti-correlation between $q$ and cluster age $t$. Finally, we suggest that stellar magnetic braking can be scaled by the entropic index $q$.Comment: 6 pages and 2 figures, accepted to EPL on October 17, 201