Fermionic vacuum polarization by an Abelian magnetic tube in the cosmic string spacetime

Abstract

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.

Scattering and bound states for the Hulthén potential in a cosmic string background

“…Nevertheless, the dominant part of these scattering studies is limited to flat spacetime and the cases regarding the curved spacetime are actually less frequent. On the other hand, the dynamics of quantum mechanics on curved spaces in the presence of topological defects has attracted much attention in recent years [27][28][29][30][31][32][33][34][35].…”

Azimuthal Fermionic Current in the Cosmic String Spacetime Induced by a Magnetic Tube

“…By the continuity condition imposed on the fermionic wave function at the boundary, it means r = a, we can related the constants C 1 and D 1 , in (25), and C (i) , in (27). After some intermediate steps we have,…”

Uma discussão sistemática sobre as cordas cósmicas e o modelo de vórtices abelianos proposto por Nielsen e Olesen

“…Compreendendo-se o vácuo como estado de menor energia, os efeitos de polarização do vácuo podem ser compreendidos como mudanças na escala dessa menor energia. Tais efeitos em teoria quântica de campos são vistos calculando os valores esperados no vácuo, VEV, de certas observáveis, tais como, a densidade de corrente induzida [25] e o tensor energia-momento dos campos de matéria [21] induzido. Tais observáveis servem como fontes para as equações de Maxwell, no caso da densidade de corrente induzida, e para as equações de Einstein, no caso do tensor energia-momento.…”

“…Estes efeitos de polarização do vácuo 2 , na teoria quântica de campos, induzidos por uma estrutura cônica, foram alvos de muitos trabalhos publicados. Na análise especifica para o VEV do tensor energia-momento T µ ν , por exemplo, podemos observar vários trabalhos publicados, levando em consideração o caso para campos escalares [14][15][16][17][18][19] e campos fermiônicos [20][21][22][23][24] interagindo com campos vetoriais [24]. Outro observável físico induzido, devidoà presença desse defeito,é a densidade de corrente e carga, que servirá como fonte para as equações de Maxwell.…”