Magnetic flux in the vacuum of quantum bosonic matter in the cosmic string background

Sitenko, Yu. A.; Gorkavenko, Volodymyr M.; Tsarenkova, Mariia S.

doi:10.1103/physrevd.106.105010

Cited by 1 publication

(2 citation statements)

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“…We conclude that relation (17) based on the direct usage of the field solutions (7) is not suitable for the computations of the vacuum polarization outside the impenetrable thin tube (𝑚𝑟 0 ≪ 1). In this case, more appropriate, in our opinion, should be the technique of computation with the help of a transformation in the complex plane, when the Bessel functions 𝐽 𝜈 (𝑦) and 𝑌 𝜈 (𝑦) transform to the modified Bessel 𝐼 𝜈 (𝑦) and Macdonald 𝐾 𝜈 (𝑦) functions, see, e.g., [31].…”

Section: Discussionmentioning

confidence: 99%

“…For the induced vacuum energy, the case of the Dirichlet boundary condition was considered in [26][27][28]. For the induced vacuum current and magnetic flux, the case of the Dirichlet boundary condition was considered in [29], the case of the Neumann boundary condition was considered in [30], and the general case for the arbitrary value of the parameter 𝜃 was considered in [31].…”

Section: Introductionmentioning

confidence: 99%

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Induced Vacuum Energy Density of Quantum Charged Scalar Matter in the Background of an Impenetrable Magnetic Tube with the Neumann Boundary Condition

Gorkavenko

Sitenko

et al. 2023

Ukr. J. Phys.

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We consider the vacuum polarization of a charged scalar matter field outside the tube with magnetic flux inside. The tube is impenetrable for quantum matter, and the perfectly rigid (Neumann) boundary condition is imposed at its surface. We write expressions for the induced vacuum energy density for the case of a space with arbitrary dimension and for an arbitrary value of the magnetic flux. We do the numerical computation for the case of a half-integer flux value in the London flux units and the (2 + 1)-dimensional space-time. We show that the induced vacuum energy of the charged scalar matter field is induced, if the Compton wavelength of the matter field exceeds the transverse size of the tube considerably. We show that the vacuum energy is periodic in the value of the magnetic flux of the tube, providing a quantumfield-theoretical manifestation of the Aharonov–Bohm effect. The dependencies of the induced vacuum energy upon the distance from the center of the tube for different values of its thickness are obtained. The results are compared to those obtained earlier in the case of the perfectly reflecting (Dirichlet) boundary condition. It is shown that the value of the induced vacuum energy density in the case of the Neumann boundary condition is greater than in the case of the Dirichlet boundary condition.

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Section: Discussionmentioning

confidence: 99%