Electromagnetic Casimir Effect in Wedge Geometry and the Energy-Momentum Tensor in Media

Brevik, Iver; Ellingsen, Simen Å.; Milton, Kimball A.

doi:10.1142/s0217751x10049542

Cited by 5 publications

(2 citation statements)

References 43 publications

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“…Calculation of the Casimir energy for configuration close to those considered in our paper has attracted much attention in recent studies. Ellingsen, Brevik, and Milton [51,52,53,54,55] calculated the vacuum energy for wedge and cylinder geometry which includes, as a special case, our cone configuration. The periodic boundary conditions in angular variable should be used for this choice.…”

Section: Discussionmentioning

confidence: 99%

Vacuum energy in conical space with additional boundary conditions

Nesterenko¹,

Pirozhenko²

2011

Class. Quantum Grav.

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Total vacuum energy of some quantized fields in conical space with additional boundary conditions is calculated. These conditions are imposed on a cylindrical surface which is coaxial with the symmetry axis of conical space. The explicit form of the matching conditions depends on the field under consideration. In the case of electromagnetic field, the perfectly conducting boundary conditions or isorefractive matching conditions are imposed on the cylindrical surface. For a massless scalar field, the semi-transparent conditions (δ-potential) on the cylindrical shell are investigated. As a result, the total Casimir energy of electromagnetic field and scalar field, per a unit length along the symmetry axis, proves to be finite unlike the case of an infinitely thin cosmic string. In these studies the spectral zeta functions are widely used. It is shown briefly how to apply this technique for obtaining the asymptotics of the relevant thermodynamical functions in the high temperature limit.

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Section: Discussionmentioning

confidence: 99%

Vacuum energy in conical space with additional boundary conditions

Nesterenko¹,

Pirozhenko²

2011

Class. Quantum Grav.

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“…As is obvious from these considerations, a general study of energy conditions in Casimir configurations requires a theoretical framework that is capable of dealing with the energy-momentum tensor in arbitrary geometries. Standard computations of Casimir energy momentum tensors 8,9,10,11,12 are usually based on mode summation/expansion, image charge methods or similar techniques which are suited for specific simple geometries. In the present work, we report on progress using the worldline approach 13 to the Casimir effect for the case of a Dirichlet scalar field 14,15 which has meanwhile been used to study a variety of nontrivial Casimir configurations 16,17,18,19 .…”

Section: Introductionmentioning

confidence: 99%

Energy-Momentum Tensors With Worldline Numerics

Schäfer

Huet

Gies

2012

Int. J. Mod. Phys. Conf. Ser.

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We apply the worldline formalism and its numerical Monte-Carlo approach to computations of fluctuation induced energy-momentum tensors. For the case of a fluctuating Dirichlet scalar, we derive explicit worldline expressions for the components of the canonical energy-momentum tensor that are straightforwardly accessible to partly analytical and generally numerical evaluation. We present several simple proof-of-principle examples, demonstrating that efficient numerical evaluation is possible at low cost. Our methods can be applied to an investigation of positive-energy conditions.

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Quantum field theory on toroidal topology: Algebraic structure and applications

Khanna

Malbouisson

et al. 2014

Physics Reports

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The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particles physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matted physics. The theory on a torus Γ d D = (S 1 ) d × R D−d is developed from a Lie-group representation and c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real-and imaginary-time versions, is addressed by focussing on its topological structure, the torus Γ 1 4 . The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac field on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on the hadronic phase structure are investigated, taking into account density and temperature. As a final application, effects of extra spatial dimensions are addressed, by developing a quantum electrodynamics in a five-dimensional space-time, where the fifth-dimension is compactified on a torus. The formalism, initially developed for particle physics, provides results compatible with other trials of probing the existence of extra-dimensions.

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Electromagnetic Casimir Effect in Wedge Geometry and the Energy-Momentum Tensor in Media

Cited by 5 publications

References 43 publications

Vacuum energy in conical space with additional boundary conditions

Vacuum energy in conical space with additional boundary conditions

Energy-Momentum Tensors With Worldline Numerics

Quantum field theory on toroidal topology: Algebraic structure and applications

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