In this paper, we consider a charged massive fermionic quantum field in the space-time of an idealized cosmic string, in the presence of a magnetic field confined in a cylindrical tube of finite radius. Three distinct configurations for the magnetic field is taken into account: (i) a cylindrical shell of radius a, (ii) a magnetic field proportional to 1/r and (iii) a constant magnetic field. In these three cases, the axis of the infinitely long tube of radius a coincides with the cosmic string. Our main objective is to analyze the induced vacuum fermionic current densities outside the tube. In order to do that, we explicitly construct the wavefunctions inside and outside the tube for each case. Having the complete set of normalized wave-functions, we use the summation method to develop our analysis. We show that in the region outside the tube, the induced currents are decomposed into a parts corresponding to a zero-thickness magnetic flux in addition to a core-induced contributions. The latter presents specific form depending on the magnetic field configuration considered. We also see that the only non-vanishing component of fermionic current corresponds to the azimuthal one. The zero-thickness contribution depends only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one. As to the core-induced contribution, it depends on the total magnetic flux inside the tube, and consequently, in general, it is not a periodic function of the flux.

We use the method of double pole QCD sum rule which is basically a fit with two exponentials of the correlation function, where we can extract the masses and decay constants of mesons as a function of the Borel mass. We apply this method to study the mesons: ρ(1S, 2S), ψ(1S, 2S), Υ(1S, 2S) and ψt(1S, 2S). We also present predictions for the toponiuns masses ψt(1S, 2S) of m(1S) = 357 GeV and m(2S) = 374 GeV.

In this paper, we consider a charged massive fermionic quantum field in the idealized cosmic string spacetime and in the presence of a magnetic field confined in a cylindrical tube of finite radius. Three distinct configurations for the magnetic fields are taken into account: (i) a cylindrical shell of radius a, (ii) a magnetic field proportional to 1/r and (iii) a constant magnetic field. In these three cases, the axis of the infinitely long tube of radius a coincides with the cosmic string. Our main objectives in this paper are to analyze the fermionic condensat (FC) e and the vacuum expectation value (VEV) of the fermionic energy-momentum tensor. In order to do that, we explicitly construct the complete set of normalized wave-functions for each configuration of magnetic field. We show that in the region outside the tube, the FC and the VEV of the energy-momentum tensor are decomposed into two parts: the first ones correspond to the zero-thickness magnetic flux contributions, and the seconds are induced by the non-trivial structure of the magnetic field, named core-induced contributions. The latter present specific forms depending on the magnetic field configuration considered. We also show that the VEV of the energymomentum tensor is diagonal, obeys the conservation condition and its trace is expressed in terms of the fermionic condensate. The zero-thickness contributions to the FC and VEV of the energy-momentum tensor, depend only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one. As to the core-induced contributions they depend on the total magnetic flux inside the tube, and consequently, in general, are not a periodic function of the magnetic flux.

Devidoà grande gama de aplicações e efeitos do modelo de vórtices abelianos de Nielsen e Olesen nas mais diversasáreas da física, que vai desde a matéria condensada até efeitos astrofísicos, faz-se necessário alguma obra na literatura que aborde este tema de forma simples e sucinta para que o estudante de graduação tanto em física, como deáreas afins, tenha a possibilidade de conhecer e compreender os mecanismos associados a este modelo de vórtices que o indicam como um forte candidatoà fonte para os defeitos topológicos tipo corda cósmica propostos por Vilenkin. Levando em consideração que este tema fica concentrado apenas majoritariamente nas pós-graduações em física, não sendo tão acessível a estudantes de graduação, desenvolvemos este trabalho fazendo uma pequena revisão sistemática noâmbito dos vórtices abelianos e como tais objetos influenciam o espaço-tempo a sua volta quando aplicadosà Relatividade Geral. Palavras-chave: Relatividade Geral, Teoria de Campos, Gravitação, Vórtices Abelianos.Due to the wide range of applications and effects of the Abelian vortex model of Nielsen and Olesen in the areas of physics, ranging from condensed matter to astrophysical effects, some work in the literature is necessary to approach this topic in a simple and succinct way that the undergraduate student in both physics and related areas has the possibility to know and understand the mechanisms associated with this vortex model that indicate him as a strong candidate for the source for the topological defects proposed by Vilenkin. Taking into account that this subject is concentrated only in postgraduate studies in physics, and is not so accessible to undergraduate students, we have developed this work by making a small systematic review in the scope of abelian vortices and how these objects influence space-time their when applied to General Relativity. Keywords: General Relativity, Field Theory, Gravitation, Abelian Votex. IntroduçãoDe acordo com a teoria do Big Bang, o universo está se expandindo e resfriando-se. Durante sua expansão, as quebras espontâneas das simetrias fundamentais levaram o universo a sofrer uma série de transições de fase. Nos modelos de física de altas energias, a formação dos defeitos topológicos, causados por essas transições, tais como paredes de domínio, monopolos e cordas cósmicas, entre outras, estão previstas a ocorrerem segundo a referência [1,2].A corda cósmica está entre os tipos de defeitos topológicos mais estudados, embora recentes observações da radiação cósmica de fundo tenham descartado-a como fonte primária para as perturbações da densidade primordial. Tal defeito, ainda sim serve como uma das contribuições dessa perturbação. Este tipo de defeito serve também como uma possível fonte para explicar um número considerável de efeitos astrofísicos, tais como: rajadas de raios gama, onde a escala de energia da corda * Endereço de correspondência: mikael.souto@ufrr.br. na qual a simetriaé quebrada, em uma escala de energia da ordem de 1014 GeV , explica a taxa, a duração e a fluência das...

Abstract:In this paper, we calculate the vacuum expectation value of the azimuthal fermionic current, associated with a massive fermionic quantum field in the spacetime of an idealized cosmic string, considering the presence of a magnetic tube of radius a, coaxial to the string. In this analysis three distinct configurations of magnetic field are considered: (i) a magnetic field concentrated on a surface of the tube; (ii) a magnetic field presenting a 1/r radial dependence; and (iii) an homogeneous magnetic field. In order to develop this analysis , we construct the complete set of normalized solution of the Dirac equation in the region outside the tube. By using the mode-sum formula, we show that the azimuthal induced current is formed by two contributions: the first being the current induced by a line of magnetic flux running along the string, and the second, named core-induced current, is induced by the non-vanishing extension of the magnetic tube. The first contribution depends only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one; as to the second contribution, it depends on the total magnetic flux. We specifically analyze the core-induced current in several limits of the parameters and distance to the tube.