Non-smoothness of the boundary and the relevant heat kernel coefficients

Nesterenko, V. V.; Pirozhenko, I. G.; Dittrich, J.

doi:10.1088/0264-9381/20/3/304

Cited by 59 publications

(58 citation statements)

References 60 publications

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“…We now must face up to the fact that our result contains an unremovable divergence, associated with the nonzero a 2 heat kernel coefficient found by Nesterenko et al [8,9]. This occurs precisely because of the m = 0 terms in Eq.…”

Section: Exterior Region Included Assuming Perfectly Conductingmentioning

confidence: 72%

“…Since that time, various embodiments of the wedge with perfectly conducting walls have been treated by Brevik and co-workers [4,5,6] and others [7]. More recently a wedge intercut by a cylindrical shell was considered by Nesterenko and collaborators, first for a semicircular wedge [8], then for arbitrary dihedral angle [9]. Local Casimir stresses were examined by Saharian and co-workers [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Exterior Region Included Assuming Perfectly Conductingmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Electrodynamic Casimir effect in a medium-filled wedge

2009

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“…The formulae for the Wightman function and the VEV of the field square in Neumann case are obtained from the corresponding formulae for Dirichlet scalar by the replacements sin(qnφ) → cos(qnφ), I qn (jx) → I ′ qn (jx), K qn (jx) → K ′ qn (jx), j = a, b, and with the term n = 0 included in the summation. In the expressions for the VEVs of the energy-momentum tensor this leads to the change of the sign for the second term in the figure braces on the right of (35) and to the change of the sign for the off-diagonal component (36).…”

Section: Resultsmentioning

confidence: 99%

“…This geometry is also interesting from the point of view of general analysis for surface divergences in the expectation values of local physical observables for boundaries with discontinuities. The nonsmoothness of the boundary generates additional contributions to the heat kernel coefficients (see, for instance, the discussion in [28,33,34,35] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries

Saharian

Tarloyan

2008

Annals of Physics

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Wightman function, the vacuum expectation values of the field square and the energymomentum tensor are investigated for a massive scalar field with general curvature coupling parameter inside a wedge with two coaxial cylindrical boundaries. It is assumed that the field obeys Dirichlet boundary condition on bounding surfaces. The application of a variant of the generalized Abel-Plana formula enables to extract from the expectation values the contribution corresponding to the geometry of a wedge with a single shell and to present the interference part in terms of exponentially convergent integrals. The local properties of the vacuum are investigated in various asymptotic regions of the parameters. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. It is shown that the interaction forces between the separate parts of the boundary are always attractive. The generalization to the case of a scalar field with Neumann boundary condition is discussed.

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“…Some effective methods for calculating vacuum energies with the help of heat kernels have been developed [16,17,18,19,20,21,22,23,24]. There are many studies on the heat kernel [25,26,27,28] and on its applications [29,30,31,32]. For spectral counting functions, in mathematics, the study sets off researches into spectral theory, with the idea of recovering geometry of a manifold from the knowledge of the eigenvalues of a differential operator [5,33].…”

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confidence: 99%

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

Dai

Xie

2010

J. High Energ. Phys.

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In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the equations for these three quantities; this allows us to achieve them by directly solving equations. In order to construct the equations, we introduce shifted local one-loop effective actions, shifted local vacuum energies, and local spectral counting functions. We solve the equations of one-loop effective actions, vacuum energies, and spectral counting functions for free massive scalar fields in R n , scalar fields in three-dimensional hyperbolic space H 3 (the Euclidean Anti-de Sitter space AdS 3 ), in H 3 /Z (the geometry of the Euclidean BTZ black hole), and in S 1 , and the Higgs model in a (1 + 1)-dimensional finite interval. Moreover, in the above cases, we also calculate the spectra from the counting functions. Besides exact solutions, we give a general discussion on approximate solutions and construct the general series expansion for one-loop effective actions, vacuum energies, and spectral counting functions. In doing this, we encounter divergences. In order to remove the divergences, renormalization procedures are used. In this approach, these three physical quantities are regarded as spectral functions in the spectral problem.

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Non-smoothness of the boundary and the relevant heat kernel coefficients

Cited by 59 publications

References 60 publications

Electrodynamic Casimir effect in a medium-filled wedge

Electrodynamic Casimir effect in a medium-filled wedge

Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

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