scholarly journals VACUUM POLARIZATION BY FERMIONIC FIELDS IN HIGHER DIMENSIONAL COSMIC STRING SPACE-TIME

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1481-1488 ◽  
Author(s):  
J. SPINELLY ◽  
E. R. BEZERRA DE MELLO
Keyword(s):  
Magnetic Flux ◽  
Cosmic String ◽  
Vacuum Polarization ◽  
Fractional Part ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Closed Expression ◽  
Fermionic Fields ◽  
Tensor Formula

In this paper we investigate vacuum polarization effects associated with charged massive quantum fermionic fields in a six-dimensional cosmic string space-times considering the presence of a magnetic flux running along its core. We have shown that for specific values of the parameters which codify the presence of the cosmic string, and the fractional part of the ratio of the magnetic flux by the quantum one, a closed expression for the respective Green function is obtained. Adopting this result, we explicitly calculate the renormalized vacuum expectation value of the energy-momentum tensor, [Formula: see text], and analyse this result in some limiting cases.

scholarly journals VACUUM POLARIZATION OF A CHARGED MASSLESS FERMIONIC FIELD BY A MAGNETIC FLUX IN THE COSMIC STRING SPACETIME

2004 ◽  
Vol 13 (04) ◽  
pp. 607-624 ◽  
Author(s):  
J. SPINELLY ◽  
E. R. BEZERRA DE MELLO
Keyword(s):  
Magnetic Flux ◽  
Cosmic String ◽  
Energy Momentum Tensor ◽  
Finite Thickness ◽  
Momentum Tensor ◽  
Homogeneous Field ◽  
Physical Systems ◽  
Left Handed ◽  
Spinor Fields ◽  
Fermionic Fields

We calculate the vacuum averages of the energy–momentum tensor associated with a massless left-handed spinor fields due to magnetic fluxes on idealized cosmic string spacetime. In this analysis three distinct configurations of magnetic fields are considered: (i) a homogeneous field inside the tube, (ii) a magnetic field proportional to 1/r, and (iii) a cylindrical shell with δ-function. In these three cases the axis of the infinitely long tubes of radius R coincides with the cosmic string. In order to proceed with these calculations we explicitly obtain the Euclidean Feynman propagators associated with these physical systems. As we shall see, these propagators possess two distinct parts. The first are the standard ones, i.e. corresponding to the spinor Green's functions associated with the massless fermionic fields on the idealized cosmic string spacetime with a magnetic flux running through the line singularity. The second parts are new, they are due to the finite thickness of the radius of the tubes. As we shall see these extra parts provide relevant contributions to the vacuum averages of the energy–momentum tensor.

scholarly journals VACUUM POLARIZATION IN A COSMIC STRING SPACETIME INDUCED BY FLAT BOUNDARY

2011 ◽  
Vol 03 ◽  
pp. 434-445
Author(s):  
EUGÊNIO R. BEZERRA DE MELLO ◽  
ARAM A. SAHARIAN
Keyword(s):  
Cosmic String ◽  
Vacuum Polarization ◽  
Energy Momentum Tensor ◽  
Neumann Boundary ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Massive Scalar ◽  
Expectation Values ◽  
Massive Scalar Field ◽  
Higher Dimensional

In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string.

scholarly journals Quantum Effects in the Spacetime of a Magnetic Flux Cosmic String

2003 ◽  
Vol 18 (12) ◽  
pp. 2093-2098 ◽  
Author(s):  
M. E. X. Guimarães ◽  
A. L. N. Oliveira
Keyword(s):  
Scalar Field ◽  
Magnetic Flux ◽  
Cosmic String ◽  
Energy Momentum Tensor ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Expectation Values ◽  
Charged Scalar ◽  
Average Value ◽  
Charged Scalar Field

In this work we compute the vacuum expectation values of the energy-momentum tensor and the average value of a massive, charged scalar field in the presence of a magnetic flux cosmic string for both zero- and finite-temperature cases.

scholarly journals Induced fermionic current in AdS spacetime in the presence of a cosmic string and a compactified dimension

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
S. Bellucci ◽  
W. Oliveira dos Santos ◽  
E. R. Bezerra de Mello
Keyword(s):  
Magnetic Flux ◽  
Cosmic String ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Axial Current ◽  
De Sitter ◽  
Twisted Field ◽  
Compact Dimension ◽  
Ads Spacetime ◽  
Current Densities

AbstractIn this paper, we consider a massive charged fermionic quantum field and investigate the current densities induced by a magnetic flux running along the core of an idealized cosmic string in the background geometry of a 5-dimensional anti-de Sitter spacetime, assuming that an extra dimension is compactified. Along the compact dimension quasi-periodicity condition is imposed on the field with a general phase. Moreover, we admit the presence of a magnetic flux enclosed by the compactified axis. The latter gives rise to Ahanorov–Bohm-like effect on the vacuum expectation value of the currents. In this setup, only azimuthal and axial current densities take place. The former presents two contributions, with the first one due to the cosmic string in a 5-dimensional AdS spacetime without compact dimension, and the second one being induced by the compactification itself. The latter is an odd function of the magnetic flux along the cosmic string and an even function of the magnetic flux enclosed by the compactified axis with period equal to the quantum flux. As to the induced axial current, it is an even function of the magnetic flux along the string’s core and an odd function of the magnetic flux enclosed by the compactification perimeter. For untwisted and twisted field along compact dimension, the axial current vanishes. The massless field case is presented as well some asymptotic limits for the parameters of the model.

scholarly journals VACUUM POLARIZATION IN THE SPACE–TIME OF A SCALAR–TENSOR COSMIC STRING

2001 ◽  
Vol 16 (24) ◽  
pp. 1565-1571 ◽  
Author(s):  
V. B. BEZERRA ◽  
R. M. TEIXEIRA FILHO ◽  
G. GREBOT ◽  
M. E. X. GUIMARÃES
Keyword(s):  
Cosmic String ◽  
Polarization Effect ◽  
Vacuum Polarization ◽  
Energy Momentum Tensor ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Space Time ◽  
Scalar Tensor Theory ◽  
Expectation Values ◽  
Tensor Theory

We study the vacuum polarization effect in the space–time generated by a magnetic flux cosmic string in the framework of a scalar–tensor theory of gravity. The vacuum expectation values of the energy–momentum tensor of a conformally coupled scalar field are calculated and the dilaton's contribution to the vacuum polarization effect is shown.

scholarly journals Fermionic vacuum polarization around a cosmic string in compactified AdS spacetime

2022 ◽  
Vol 2022 (01) ◽  
pp. 010
Author(s):  
S. Bellucci ◽  
W. Oliveira dos Santos ◽  
E.R. Bezerra de Mello ◽  
A.A. Saharian
Keyword(s):  
Energy Density ◽  
Cosmic String ◽  
Vacuum Energy ◽  
Energy Momentum Tensor ◽  
Minkowski Spacetime ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Vacuum Energy Density ◽  
Ads Spacetime

Abstract We investigate topological effects of a cosmic string and compactification of a spatial dimension on the vacuum expectation value (VEV) of the energy-momentum tensor for a fermionic field in (4+1)-dimensional locally AdS spacetime. The contribution induced by the compactification is explicitly extracted by using the Abel-Plana summation formula. The mean energy-momentum tensor is diagonal and the vacuum stresses along the direction perpendicular to the AdS boundary and along the cosmic string are equal to the energy density. All the components are even periodic functions of the magnetic fluxes inside the string core and enclosed by compact dimension, with the period equal to the flux quantum. The vacuum energy density can be either positive or negative, depending on the values of the parameters and the distance from the string. The topological contributions in the VEV of the energy-momentum tensor vanish on the AdS boundary. Near the string the effects of compactification and gravitational field are weak and the leading term in the asymptotic expansion coincides with the corresponding VEV in (4+1)-dimensional Minkowski spacetime. At large distances, the decay of the cosmic string induced contribution in the vacuum energy-momentum tensor, as a function of the proper distance from the string, follows a power law. For a cosmic string in the Minkowski bulk and for massive fields the corresponding fall off is exponential. Within the framework of the AdS/CFT correspondence, the geometry for conformal field theory on the AdS boundary corresponds to the standard cosmic string in (3+1)-dimensional Minkowski spacetime compactified along its axis.

scholarly journals Fermionic condensate and the Casimir effect in cosmic string spacetime

2017 ◽  
Vol 26 (07) ◽  
pp. 1750064 ◽  
Author(s):  
A. Kh. Grigoryan ◽  
A. R. Mkrtchyan ◽  
A. A. Saharian
Keyword(s):  
Energy Density ◽  
Cosmic String ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Vacuum Energy Density ◽  
Casimir Forces ◽  
Massless Field

We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy–momentum tensor for a massive fermionic field. As geometry of boundaries we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel–Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-induced parts in both the fermionic condensate and the energy–momentum tensor vanish on the cosmic string. Fermionic condensate is positive near the string and negative at large distances, whereas the vacuum energy density is negative everywhere. The radial stress is equal to the energy density. For a massless field, the boundary-induced contribution in the VEV of the energy–momentum tensor is different from zero in the region between the plates only and it does not depend on the coordinate along the string axis. In the region between the plates and at large distances from the string, the decay of the topological part is exponential for both massive and massless fields. This behavior is in contrast to that for the VEV of the energy–momentum tensor in the boundary-free geometry with the power law decay for a massless field. The vacuum pressure on the plates is inhomogeneous and vanishes at the location of the string. The corresponding Casimir forces are attractive.

scholarly journals Vacuum Polarization in a Zero-Width Potential: Self-Adjoint Extension

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 127
Author(s):  
Yuri V. Grats ◽  
Pavel Spirin
Keyword(s):  
Scalar Field ◽  
Vacuum Polarization ◽  
Dimensional Regularization ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Field Approximation ◽  
Dimensional Euclidean Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Adjoint Extension

The effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions are analyzed. The “physical” approach consists in the usage of direct delta-potential as a model of pointlike interaction. We use the Perturbation theory in the Fourier space with dimensional regularization of the momentum integrals. In the weak-field approximation, we compute the effects of interest. The “mathematical” approach implies the self-adjoint extension technique. In the Quantum-Field-Theory framework we consider the massless scalar field in a 3-dimensional Euclidean space with an extracted point. With appropriate boundary conditions it is considered an adequate mathematical model for the description of a pointlike source. We compute the renormalized vacuum expectation value ⟨ϕ2(x)⟩ren of the field square and the renormalized vacuum averaged of the scalar-field’s energy-momentum tensor ⟨Tμν(x)⟩ren. For the physical interpretation of the extension parameter we compare these results with those of perturbative computations. In addition, we present some general formulae for vacuum polarization effects at large distances in the presence of an abstract weak potential with finite-sized compact support.

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