Casimir Effect for a Perfectly Conducting Wedge

Brevik, Iver; Lygren, M.

doi:10.1006/aphy.1996.0111

Cited by 69 publications

(66 citation statements)

References 17 publications

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“…(These results were later discussed in Ref. [213].) Although for perfectly conducting flat surfaces, the energy density is finite, for electromagnetism the individual electric and magnetic fields have divergent RMS values,…”

Section: Surface and Volume Divergencesmentioning

confidence: 83%

The Casimir effect: recent controversies and progress

Milton

2004

J. Phys. A: Math. Gen.

462

504

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Abstract. The phenomena implied by the existence of quantum vacuum fluctuations, grouped under the title of the Casimir effect, are reviewed, with emphasis on new results discovered in the past four years. The Casimir force between parallel plates is rederived as the strong-coupling limit of δ-function potential planes. The role of surface divergences is clarified. A summary of effects relevant to measurements of the Casimir force between real materials is given, starting from a geometrical optics derivation of the Lifshitz formula, and including a rederivation of the Casimir-Polder forces. A great deal of attention is given to the recent controversy concerning temperature corrections to the Casimir force between real metal surfaces. A summary of new improvements to the proximity force approximation is given, followed by a synopsis of the current experimental situation. New results on Casimir self-stress are reported, again based on δ-function potentials. Progress in understanding divergences in the self-stress of dielectric bodies is described, in particular the status of a continuing calculation of the self-stress of a dielectric cylinder. Casimir effects for solitons, and the status of the so-called dynamical Casimir effect, are summarized. The possibilities of understanding dark energy, strongly constrained by both cosmological and terrestrial experiments, in terms of quantum fluctuations are discussed. Throughout, the centrality of quantum vacuum energy in fundamental physics in emphasized.

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Section: Surface and Volume Divergencesmentioning

confidence: 83%

The Casimir effect: recent controversies and progress

Milton

2004

J. Phys. A: Math. Gen.

462

504

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“…Therefore the objections against using this formula brought up in Ref. [3] are obviously not applicable here. As a result, we obtain…”

Section: Local Zeta Function For Perfectly Conducting Wedgementioning

confidence: 96%

“…It is discussed in the literature for a long time (see, for example, Refs. [2,3,21]). When defining the global quantities in the problem at hand, we simply introduce a cutoff at the lower limit of integration over r. Thus for the total energy we have…”

Section: Local Zeta Function For Perfectly Conducting Wedgementioning

confidence: 99%

Casimir Effect for a Perfectly Conducting Wedge in Terms of Local Zeta Function

2002

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The vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of calculations and gives rise to a finite expression for the energy density in question without any subtractions. Employment of the Hertz potentials for constructing the general solution to the Maxwell equations results in a considerable simplification of the calculations. Transition to the global zeta function is carried out by introducing a cutoff nearby the cusp at the origin. Proceeding from this the heat kernel coefficients are calculated and the high temperature asymptotics of the Helmholtz free energy and of the torque of the Casimir forces are found. The wedge singularity gives rise to a specific high temperature behaviour ∼ T 2 of the quantities under consideration. The obtained results are directly applicable to the free energy of a scalar massless field and electromagnetic field on the background of a cosmic string.

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“…3) with the electromagnetic energy-momentum in the wedge [2,3,4] T µν = 1 720π 2 r 4 π 2 α 2 + 11 π 2 α 2 − 1 diag(1, −3, 1, 1), (1.4) we see that β corresponds to p. Hence the deficit angle Φ corresponds to 2π − 2α. We shall return to this analogy later.…”

Section: Introductionmentioning

confidence: 94%

Electrodynamic Casimir effect in a medium-filled wedge

2009

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We re-examine the electrodynamic Casimir effect in a wedge defined by two perfect conductors making dihedral angle α = π/p. This system is analogous to the system defined by a cosmic string. We consider the wedge region as filled with an azimuthally symmetric material, with permittivity/permeability ε1, µ1 for distance from the axis r < a, and ε2, µ2 for r > a. The results are closely related to those for a circular-cylindrical geometry, but with non-integer azimuthal quantum number mp. Apart from a zero-mode divergence, which may be removed by choosing periodic boundary conditions on the wedge, and may be made finite if dispersion is included, we obtain finite results for the free energy corresponding to changes in a for the case when the speed of light is the same inside and outside the radius a, and for weak coupling, |ε1 − ε2| ≪ 1, for purely dielectric media. We also consider the radiation produced by the sudden appearance of an infinite cosmic string, situated along the cusp line of the pre-existing wedge.

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Casimir Effect for a Perfectly Conducting Wedge

Cited by 69 publications

References 17 publications

The Casimir effect: recent controversies and progress

The Casimir effect: recent controversies and progress

Casimir Effect for a Perfectly Conducting Wedge in Terms of Local Zeta Function

Electrodynamic Casimir effect in a medium-filled wedge

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