Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations

Using appropriate harmonics, we study the future asymptotic behavior of massless scalar fields on a class of cosmological vacuum spacetimes. The spatial manifold is assumed to be a circle bundle over a higher genus surface with a locally homogeneous metric. Such a manifold corresponds to the SL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi III type). After a technical preparation including an introduction of suitable harmonics for the circle-fibered Bianchi VIII to separate variables, we derive systems of ordinary differential equations for the scalar field. We present future asymptotic solutions for these equations in a special case, and find that there is a close similarity with those on the circle-fibered Bianchi III spacetime. We discuss implications of this similarity, especially to (gravitational) linear perturbations. We also point out that this similarity can be explained by the "fiber term dominated behavior" of the two models.Comment: 23 pages, no figures, to be published in Class. Quant. Gravi

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

On the equivalence of two deformation schemes in quantum field theory

Two recent deformation schemes for quantum field theories on the two-dimensional Minkowski space, making use of deformed field operators and Longo-Witten endomorphisms, respectively, are shown to be equivalent.Comment: 14 pages, no figure. The final version is available under Open Access. CC-B

Unitary vertex algebras and Wightman conformal field theories

We prove an equivalence between the following notions: (i) unitary Mobius vertex algebras, and (ii) Wightman conformal field theories on the circle (with finite-dimensional conformal weight spaces) satisfying an additional condition that we call uniformly bounded order. Reading this equivalence in one direction, we obtain new analytic and operator-theoretic information about vertex operators. In the other direction we characterize OPEs of Wightman fields and show they satisfy the axioms of a vertex algebra. As an application we establish new results linking unitary vertex operator algebras with conformal nets

Future asymptotic expansions of Bianchi VIII vacuum metrics

Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and in a previous article we analyzed the asymptotic behaviour of solutions in these variables. One objective of this paper is to give an asymptotic expansion for the metric. Furthermore, we relate this expansion to the topology of the compactified spatial hypersurfaces of homogeneity. The compactified spatial hypersurfaces have the topology of Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII spacetimes, the length of a circle fibre converges to a positive constant but that in the case of general Bianchi VIII solutions, the length tends to infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces correcte

Neutrino masses and mixing from S4 flavor twisting

We discuss a neutrino mass model based on the S4 discrete symmetry where the symmetry breaking is triggered by the boundary conditions of the bulk right-handed neutrino in the fifth spacial dimension. While the symmetry restricts bare mass parameters to flavor-diagonal forms, the viable mixing angles emerge from the wave functions of the Kaluza-Klein modes which carry symmetry breaking effect. The magnitudes of the lepton mixing angles, especially the reactor angle is related to the neutrino mass patterns and the model will be tested in future neutrino experiments, e.g., an early (late) discovery of the reactor angle favors the normal (inverted) hierarchy. The size of extra dimension has a connection to the possible mass spectrum; a small (large) volume corresponds to the normal (inverted) mass hierarchy.Comment: 22 pages, 3 figures; added references for section

Democratic Neutrino Mixing and Radiative Corrections

The renormalization effect on a specific ansatz of lepton mass matrices, arising naturally from the breaking of flavor democracy for charged leptons and that of mass degeneracy for light neutrinos, is studied from a superhigh energy scale M_0 \sim 10^{13} GeV to the electroweak scale in the framework of the minimal supersymmetric standard model. We find that the democratic neutrino mixing pattern obtained from this ansatz may in general be instable against radiative corrections. With the help of similar flavor symmetries we prescribe a slightly different scheme of lepton mass matrices at the scale M_0, from which the democratic mixing pattern of lepton flavors can be achieved, after radiative corrections, at the experimentally accessible scales.Comment: RevTex 8 pages. Phys. Rev. D (in printing

Identificação das Oportunidades de Desenvolvimento de Alianças Estratégicas a partir da Análise dos Stakeholders: um estudo em uma IES paraense.

O presente estudo tem como objetivo identificar as oportunidades de desenvolvimento de alianças estratégicas a partir da analise dos stakeholders de uma IES que atua na Região Metropolitana de Belém desde o primeiro semestre do ano de 2000 e que, hoje, oferta cinco cursos superiores para esta região. Utilizou o método de estudo de caso do tipo qualiquantitativo (Yin, 2005) para identificar e classificar os stakeholders da IES estudada com base nos estudos de Mitchell, Agle e Wood (1997) e Yoshino e Rangan (1996); como instrumentos de coleta de dados foram utilizados entrevista semi-estruturada (para os dados qualitativos) e questionário (dados quantitativos). Os resultados identificaram três grupos de stakeholders passíveis de ser formada aliança estratégica (clientes institucionais, Fundação Getúlio Vargas e os Parceiros Técnico-Científicos) e dois tipos de alianças possíveis de ser formadas (pré-competitiva e pró-competitiva). A conclusão apresentada é que a IES sob análise tem oportunidade de desenvolver alianças estratégicas do tipo pré-competitiva (com os clientes institucionais e parceiros técnico-científicos) e pró-competitiva (Fundação Getúlio Vargas) com seus stakeholders definitivos com o intuito de melhorar a sua competitividade no mercado da região metropolitana de Belém

Mathematics Indicates That an HIV-Style Strategy Could Be Applied to Manage the Coronavirus

We have learned to live with many potentially deadly viruses for which there is no vaccine, no immunity, and no cure. We do not live in constant fear of these viruses, instead, we have learned how to outsmart them and reduce the harm they cause. A new mathematical model that combines the spread of diseases that do not confer immunity together with the evolution of human behaviors indicates that we may be able to fight new diseases with the same type of strategy we use to fight viruses like HIV.Comment: This article is available open access online here: https://link.springer.com/chapter/10.1007%2F16618_2020_2

Tri-Bimaximal Mixing from Twisted Friedberg-Lee Symmetry

We investigate the Friedberg-Lee (FL) symmetry and its promotion to include the $\mu - \tau$ symmetry, and call that the twisted FL symmetry.Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing.In the first scheme, we suggest the semi-uniform translation of the FL symmetry.The second one is based on the $S_3$ permutation family symmetry.The breaking terms, which are twisted FL symmetric, are introduced.Some viable models in each scheme are also presented.Comment: 14 pages, no figure. v2: 16 pages, modified some sentences, appendix added, references added. v3: 14 pages, composition simplified, accepted version in EPJ