CASIMIR ENERGY AND FORCE INDUCED BY AN IMPENETRABLE FLUX TUBE OF FINITE RADIUS

A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady). The Casimir energy and force are periodic in the value of the magnetic flux, being independent of the coupling to the space–time curvature scalar. We conclude that a topological defect of the vortex type can polarize the vacuum of only those quantum fields that have masses which are much less than a scale of the spontaneous symmetry breaking.

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VACUUM POLARIZATION BY A MAGNETIC FIELD IN THE COSMIC STRING SPACETIME

International Journal of Modern Physics A ◽

10.1142/s0217751x02013447 ◽

2002 ◽

Vol 17 (29) ◽

pp. 4375-4384 ◽

Cited By ~ 17

Author(s):

J. SPINELLY ◽

E. R. BEZERRA DE MELLO

Keyword(s):

Magnetic Field ◽

Cosmic String ◽

Vacuum Polarization ◽

Cylindrical Tube ◽

Field Operator ◽

Massless Scalar ◽

Finite Radius ◽

Polarization Effects ◽

Scalar Quantum ◽

Bohm Effect

In this paper we consider a charged massless scalar quantum field operator in the spacetime of an idealized cosmic string which presents a magnetic field confined in a cylindrical tube of finite radius. Three distinct situations are taken into account in this analysis. In three cases the axis of the infinitely long tube of radius R coincides with the cosmic string. Because we study the combined gravitational and electromagnetic Aharanov-Bohm effect, we calculate the vacuum polarization effects outside the tube.

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DIRAC FIELDS IN THE BACKGROUND OF A MAGNETIC FLUX STRING AND SPECTRAL BOUNDARY CONDITIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x99002232 ◽

1999 ◽

Vol 14 (30) ◽

pp. 4749-4761 ◽

Cited By ~ 15

Author(s):

C. G. BENEVENTANO ◽

M. DE FRANCIA ◽

E. M. SANTANGELO

Keyword(s):

Magnetic Flux ◽

Boundary Conditions ◽

Index Theorem ◽

Casimir Energy ◽

The Self ◽

Dirac Field ◽

Finite Region ◽

Finite Radius ◽

Dirac Fields ◽

Aharonov Bohm

We study the problem of a Dirac field in the background of an Aharonov–Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behavior of the eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and evaluate its vacuum fermionic number and Casimir energy.

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VACUUM CURRENTS AROUND A MAGNETIC FLUX STRING

International Journal of Modern Physics A ◽

10.1142/s0217751x91002501 ◽

1991 ◽

Vol 06 (29) ◽

pp. 5327-5347 ◽

Cited By ~ 35

Author(s):

E.G. FLEKKØY ◽

J.M. LEINAAS

Keyword(s):

Magnetic Flux ◽

Exact Solutions ◽

Vacuum Polarization ◽

Local Effects ◽

Polarization Effects ◽

Dirac Equations ◽

Dimensional Effects ◽

Current Densities

We examine vacuum polarization effects around a singular magnetic flux string in 2+1 and 3+1 dimensions. In particular we determine the local effects: charge and current densities and the flux induced by the vacuum current. The analysis is performed entirely on the basis of exact solutions to the pertinent Dirac equations, and we find that the (3+1)-dimensional effects can be described in a simple way as a superposition of the (2+1)-dimensional effects.

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VACUUM ENERGY INDUCED BY AN IMPENETRABLE FLUX TUBE OF FINITE RADIUS

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194511001474 ◽

2011 ◽

Vol 03 ◽

pp. 375-385

Author(s):

V. M. GORKAVENKO ◽

YU. A. SITENKO ◽

O. B. STEPANOV

Keyword(s):

Magnetic Field ◽

Vacuum Energy ◽

Dirichlet Boundary ◽

Vacuum Energy Density ◽

Transverse Size ◽

Massive Scalar ◽

Curvature Scalar ◽

Finite Radius ◽

Massive Scalar Field ◽

The Magnetic Field

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the tube. The vacuum energy is induced, being periodic in the value of the magnetic flux enclosed in the tube. The dependence of the vacuum energy density on the distance from the tube and on the coupling to the space-time curvature scalar is comprehensively analyzed.

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