Bessel ζ-function approach to the Casimir effect of a scalar field in a spherical bag

Romeo, August

doi:10.1103/physrevd.52.7308

Cited by 29 publications

(32 citation statements)

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“…superconductors [28]) -other applications are shown in [29].Many of these advances came true by means of a precise knowledge of the spectral zeta function associated to each system, which is the key to the derivation of many results. Somehow, this happens also to the present paper: our calculation is indebted to the investigation started in [30,31] about Bessel zeta functions [33,34], and taken further in [38] for the case of a purely scalar field inside a sphere, under Dirichlet boundary conditions. That work is here extended so as to include all the field modes appearing in the problems under discussion.…”

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Complete Zeta-Function Approach to the Electromagnetic Casimir Effect for Spheres and Circles

1996

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A technique for evaluating the electromagnetic Casimir energy in situations involving spherical or circular boundaries is presented. Zeta function regularization is unambiguously used from the start and the properties of Bessel and related zeta functions are central. Nontrivial results concerning these functions are given. While part of their application agrees with previous knowledge, new results like the zeta-regularized electromagnetic Casimir energy for a circular wire are included.

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“…As for d(D, l), we find its value in [44] and put 7) and the form of the A k (D)'s can be read off from [45] (see also [38]). [30] and [31] we showed how to obtain an integral representation valid for −1 < Re s < 0, which reads…”

Section: )mentioning

confidence: 99%

Complete Zeta-Function Approach to the Electromagnetic Casimir Effect for Spheres and Circles

1996

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“…The residue is simply formula (4.16), while the finite parts have been obtained through numerical evaluation of (4.13) by the methods described in refs. [29,30]. Fig.…”

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confidence: 98%

Influence of a Magnetic Fluxon on the Vacuum Energy of Quantum Fields Confined by a Bag

Romeo¹

1998

Communications in Mathematical Physics

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We study the simultaneous influence of boundary conditions and external fields on quantum fluctuations by considering vacuum zero-point energies for quantum fields in the presence of a magnetic fluxon confined by a bag, circular and spherical for bosons and circular for fermions. The Casimir effect is calculated in a generalized cut-off regularization after applying zeta-function techniques to eigenmode sums and using recent techniques about Bessel zeta functions at negative arguments. *

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“…In particular, the generalized zeta function method [19,20] is in general very powerful to give physical meaning to the divergent quantities. There are several examples of the application of this method to the evaluation of the Casimir effect (see, for instance, [7,20,21,22,23,24,25,26,27,28,29,30]). In this paper, by using the zeta function technique, we consider the Casimir energy for the geometries of a single and two parallel plates, moving by uniform proper acceleration through the Fulling-Rindler vacuum.…”

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confidence: 99%

Casimir energy in the Fulling-Rindler vacuum

2004

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The Casimir energy is evaluated for massless scalar fields under Dirichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on one and two infinite parallel plates moving by uniform proper acceleration through the Fulling-Rindler vacuum in an arbitrary number of spacetime dimension. For the geometry of a single plate both regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are considered. The zeta function technique is used, in combination with contour integral representations. The Casimir energies for separate RR and RL regions contain pole and finite contributions. For an infinitely thin plate taking RR and RL regions together, in odd spatial dimensions the pole parts cancel and the Casimir energy for the whole Rindler wedge is finite. In d = 3 spatial dimensions the total Casimir energy for a single plate is negative for Dirichlet scalar and positive for Neumann scalar and the electromagnetic field. The total Casimir energy for two plates geometry is presented in the form of a sum of the Casimir energies for separate plates plus an additional interference term. The latter is negative for all values of the plates separation for both Dirichlet and Neumann scalars, and for the electromagnetic field.

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Bessel ζ-function approach to the Casimir effect of a scalar field in a spherical bag

Abstract: A mode-summation technique based on the Bessel spectral < function is developed. As an example, we evaluate the finite part of the regularized zero-point energy for a massless scalar field confined in the interior of a spherical region. PACS number(s): 03.65.Ge, 02.30.Dk

Cited by 29 publications

References 29 publications

Complete Zeta-Function Approach to the Electromagnetic Casimir Effect for Spheres and Circles

Complete Zeta-Function Approach to the Electromagnetic Casimir Effect for Spheres and Circles

Influence of a Magnetic Fluxon on the Vacuum Energy of Quantum Fields Confined by a Bag

Casimir energy in the Fulling-Rindler vacuum

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