Editorial

2 pages, 161 KiB

Open AccessEditorial

by Kimball Milton and Iver Brevik

Symmetry 2019, 11(2), 201; https://doi.org/10.3390/sym11020201 - 11 Feb 2019

Cited by 5 | Viewed by 1716

Casimir physics encompasses all phenomena that are due to quantum field fluctuations in
nontrivial backgrounds, which might be gravitational, curved space, electromagnetic (background
fields or dielectric materials) [...] Full article

(This article belongs to the Special Issue Casimir Physics and Applications)

Research

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10 pages, 789 KiB

Open AccessFeature PaperArticle

Dispersion Forces Between Fields Confined to Half Spaces

by M. Bordag and I.G. Pirozhenko

Symmetry 2018, 10(3), 74; https://doi.org/10.3390/sym10030074 - 19 Mar 2018

Cited by 2 | Viewed by 2462

Abstract

We consider the Casimir effect for a scalar field interacting with another scalar field that is confined to two half spaces. This model is aimed to mimic the interaction of the photon field with matter in two slabs. We use Dirichlet boundary conditions [...] Read more.

We consider the Casimir effect for a scalar field interacting with another scalar field that is confined to two half spaces. This model is aimed to mimic the interaction of the photon field with matter in two slabs. We use Dirichlet boundary conditions on the interfaces for the fields in the half spaces and calculate their one-loop contribution to the wave equation for the other field. We perform the ultraviolet renormalization and develop a convenient formalism for the calculation of the vacuum energy in this configuration. Full article

(This article belongs to the Special Issue Casimir Physics and Applications)

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10 pages, 397 KiB

Open AccessArticle

Casimir Energies for Isorefractive or Diaphanous Balls

by Kimball A. Milton and Iver Brevik

Symmetry 2018, 10(3), 68; https://doi.org/10.3390/sym10030068 - 16 Mar 2018

Cited by 4 | Viewed by 2878

Abstract

It is known that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside [...] Read more.

It is known that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with

ε μ = 1

, a so-called isorefractive or diaphanous ball. Here we re-examine that example and attempt to extend it to an electromagnetic

δ

-function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented. Full article

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14 pages, 3049 KiB

Open AccessArticle

The Impact of the Anisotropy of the Media between Parallel Plates on the Casimir Force

by Gang Deng, Ling Pei, Ni Hu, Yang Liu and Jin-Rong Zhu

Symmetry 2018, 10(3), 61; https://doi.org/10.3390/sym10030061 - 07 Mar 2018

Cited by 3 | Viewed by 2783

Abstract

Quantum fluctuations of the electromagnetic field give rise to the force between parallel plates: the Casimir force. We theoretically calculate the Casimir force between two parallel isotropic plates when the space between the plates is filled with anisotropic material. Our result shows that [...] Read more.

Quantum fluctuations of the electromagnetic field give rise to the force between parallel plates: the Casimir force. We theoretically calculate the Casimir force between two parallel isotropic plates when the space between the plates is filled with anisotropic material. Our result shows that the Casimir force, especially in the direction of the force, can be significantly affected by the anisotropy of the intervening material. We also discuss the combined influence of dispersion and anisotropy, and analyze the impact of the external electric filed on the Casimir force by affecting the anisotropy of the intervening material by Kerr electro-optical effect. Full article

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16 pages, 291 KiB

Open AccessFeature PaperArticle

Renormalization for a Scalar Field in an External Scalar Potential

by Stephen A. Fulling, Thomas E. Settlemyre and Kimball A. Milton

Symmetry 2018, 10(3), 54; https://doi.org/10.3390/sym10030054 - 27 Feb 2018

Cited by 12 | Viewed by 3102

Abstract

The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background [...] Read more.

The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here, this is demonstrated in detail for two different models of the field-potential coupling. There is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully-interacting quantum field theories; these terms are finite, but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply-rising smooth potential. Full article

(This article belongs to the Special Issue Casimir Physics and Applications)

20 pages, 967 KiB

Open AccessArticle

Local Casimir Effect for a Scalar Field in Presence of a Point Impurity

by Davide Fermi and Livio Pizzocchero

Symmetry 2018, 10(2), 38; https://doi.org/10.3390/sym10020038 - 26 Jan 2018

Cited by 12 | Viewed by 3325

Abstract

The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini have considered some configurations involving delta-type [...] Read more.

The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini have considered some configurations involving delta-type potentials concentrated at points of

R^{3}

; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on

R^{3} \ {0}

, with self-adjoint boundary conditions at the origin for the Laplacian. However, the above authors have discussed only global aspects of the Casimir effect, focusing their attention on the vacuum expectation value (VEV) of the total energy. In the present paper we analyze the local Casimir effect with a point delta-type potential, computing the renormalized VEV of the stress-energy tensor at any point of

R^{3} \ {0}

; for this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours. Full article

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11 pages, 555 KiB

Open AccessFeature PaperArticle

Accounting for Dissipation in the Scattering Approach to the Casimir Energy

by Romain Guérout, Gert-Ludwig Ingold, Astrid Lambrecht and Serge Reynaud

Symmetry 2018, 10(2), 37; https://doi.org/10.3390/sym10020037 - 26 Jan 2018

Cited by 6 | Viewed by 3401

Abstract

We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that [...] Read more.

We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that the Casimir energy is given by a scattering formula expressed in terms of the scattering amplitudes coupling internal channels and taking dissipation into account implicitly. We prove that this formula is also valid when the surrounding medium is dissipative. Full article

(This article belongs to the Special Issue Casimir Physics and Applications)

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16 pages, 422 KiB

Open AccessArticle

Gluing Formula for Casimir Energies

by Klaus Kirsten and Yoonweon Lee

Symmetry 2018, 10(1), 31; https://doi.org/10.3390/sym10010031 - 21 Jan 2018

Cited by 3 | Viewed by 3282

Abstract

We provide a completely new perspective for the analysis of Casimir forces in very general piston configurations. To this end, in order to be self-contained, we prove a “gluing formula” well known in mathematics and relate it with Casimir forces in piston configurations. [...] Read more.

We provide a completely new perspective for the analysis of Casimir forces in very general piston configurations. To this end, in order to be self-contained, we prove a “gluing formula” well known in mathematics and relate it with Casimir forces in piston configurations. At the center of our description is the Dirichlet-to-Neumann operator, which encodes all the information about those forces. As an application, the results for previously considered piston configurations are reproduced in a streamlined fashion. Full article

(This article belongs to the Special Issue Casimir Physics and Applications)

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