Casimir effect for a self-interacting scalar field

Ford, L. H.

doi:10.1098/rspa.1979.0130

Cited by 67 publications

(13 citation statements)

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“…Moreover the two-loop radiative corrections for some effective field theories have been investigated in [6,7,8]. Next, in the case of a real massive scalar field NLO correction to the energy has been computed in [9,10,11,12,13,14,15,16]. This correction is a two loop correction in this case but is O(λ).…”

Section: Introductionmentioning

confidence: 99%

The Dirichlet Casimir effect for ϕ⁴theory in (3 + 1) dimensions: a new renormalization approach

Moazzemi

Namdar

Gousheh

2007

J. High Energy Phys.

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We calculate the next to the leading order Casimir effect for a real scalar field, within φ 4 theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.

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Section: Introductionmentioning

confidence: 99%

The Dirichlet Casimir effect for ϕ⁴theory in (3 + 1) dimensions: a new renormalization approach

Moazzemi

Namdar

Gousheh

2007

J. High Energy Phys.

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“…In the paper by Kong and Ravndal [2] the same boundary conditions as here are studied with the help of a different method, namely some effective field theory and the Euler-Heisenberg Lagrangian. Their result, E 4 , is of one order α smaller than (9). The renormalization has also been discussed in the paper [4].…”

Section: Introductionmentioning

confidence: 86%

“…Their result, E 4 , is of one order α smaller than (9). The renormalization has also been discussed in the paper [4].…”

Section: Introductionmentioning

confidence: 86%

Radiative correction to the Casimir force on a sphere

Bordag

Lindig

1998

Phys. Rev. D

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The first radiative correction to the Casimir energy of a perfectly conducting spherical shell is calculated. The calculation is performed in the framework of covariant perturbation theory with the boundary conditions implemented as constraints. The formalism is briefly reviewed and its use is explained by deriving the known results for two parallel planes.The ultraviolet divergencies are shown to have the same structure as those for a massive field in zeroth order of α. In the zeta-functional regularization employed by us no divergencies appear.If the radius of the sphere is large compared to the Compton wavelength of the electron the radiative correction is of order α/(R 2 m e ) and contains a logarithmic dependence on m e R. It has the opposite sign but the same order of magnitude as in the case of two parallel planes.

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“…The first attempt to calculate the radiative correction to the Casimir energy of electromagnetic field was conducted by Bordag et al [8,9]. Later, several attempts were made in a radiative correction to the Casimir energy for other quantum fields with multiple boundary conditions [10,11,12,13,14]. In this category of problems, a renormalization program is typically used to renormalize the bare parameters.…”

Section: Introductionmentioning

confidence: 99%

The Dirichlet Casimir energy for ϕ ⁴ theory in a rectangular waveguide

Valuyan¹

2018

J. Phys. G: Nucl. Part. Phys.

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In this paper, we presented the zero-and first-order radiative corrections to the Casimir energy for a massive scalar field confined with Dirichlet boundary condition in an open-ended rectangular waveguide. In the calculation procedure, we applied a systematic renormalization program that allows all influences imposed by dominant boundary conditions in a problem be automatically reflected in the counterterms, leading the counterterms to be obtained in a position-dependent manner. To remove the appeared divergences in the computation task, the Box Subtraction Scheme as a regularization technique was used. In this regularization technique, usually, two similar configurations were introduced. Then, to find the Casimir energy, the zero point energies of these two configurations were subtracted from each other via defining appropriate limits. In the present work, first, the leading-order Casimir energy for the massive scalar field in a waveguide is briefly presented. Next, by applying this renormalization and regularization procedures, the first-order radiative correction to the Casimir energy in the waveguide is calculated. Finally, all the necessary limits of the obtained answers for massive and massless cases are computed and the consistency of the obtained results are discussed.

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Casimir effect for a self-interacting scalar field

Abstract: The effect of a Ao 4 self-interaction upon the vacuum energy of a scalar field in flat space-times with boundaries and in the Einstein universe is investigated.

Cited by 67 publications

References 6 publications

The Dirichlet Casimir effect for ϕ⁴theory in (3 + 1) dimensions: a new renormalization approach

The Dirichlet Casimir effect for ϕ⁴theory in (3 + 1) dimensions: a new renormalization approach

Radiative correction to the Casimir force on a sphere

The Dirichlet Casimir energy for ϕ ⁴ theory in a rectangular waveguide

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Casimir effect for a self-interacting scalar field

Abstract: The effect of a Ao 4 self-interaction upon the vacuum energy of a scalar field in flat space-times with boundaries and in the Einstein universe is investigated.

Cited by 67 publications

References 6 publications

The Dirichlet Casimir effect for ϕ4theory in (3 + 1) dimensions: a new renormalization approach

The Dirichlet Casimir effect for ϕ4theory in (3 + 1) dimensions: a new renormalization approach

Radiative correction to the Casimir force on a sphere

The Dirichlet Casimir energy for ϕ 4 theory in a rectangular waveguide

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Product

Resources

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The Dirichlet Casimir effect for ϕ⁴theory in (3 + 1) dimensions: a new renormalization approach

The Dirichlet Casimir effect for ϕ⁴theory in (3 + 1) dimensions: a new renormalization approach

The Dirichlet Casimir energy for ϕ ⁴ theory in a rectangular waveguide