Boundary conditions as mass generation mechanism for real scalar fields

Nogueira, José Alexandre; Barbieri, Pedro

doi:10.1590/s0103-97332002000400022

Cited by 9 publications

(6 citation statements)

References 27 publications

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“…This statement necessities using the position-dependent counter-terms instead of free counter-terms in the renormalization program. This viewpoint on renormalization program has been explained in detail in previous studies [20][21][22][23][24][25][26][27] and all their physical aspects and advantages have been discussed. The same idea in the renormalization of interacting quantum field theory in the curved space time has been extensively investigated [28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Radiative correction to the Casimir energy for massive scalar field on a spherical surface

Valuyan

2017

Mod. Phys. Lett. A

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In this paper, the first order radiative correction to the Casimir energy for a massive scalar field in the φ 4 theory on a spherical surface with S 2 topology was calculated. In common methods for calculating the radiative correction to the Casimir energy, the counter-terms related to free theory are used. However, in this study, by using a systematic perturbation expansion, the obtained counterterms in renormalization program were automatically position-dependent. We maintained that this dependency was permitted, reflecting the effects of the boundary conditions imposed or background space in the problem. Additionally, along with the renormalization program, a supplementary regularization technique that we named Box Subtraction Scheme (BSS) was performed. This scheme presents a useful method for the regularization of divergences, providing a situation that the infinities would be removed spontaneously without any ambiguity. Analysis of the necessary limits of the obtained results for the Casimir energy of the massive and massless scalar field confirmed the appropriate and reasonable consistency of the answers.

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Section: Introductionmentioning

confidence: 99%

Radiative correction to the Casimir energy for massive scalar field on a spherical surface

Valuyan

2017

Mod. Phys. Lett. A

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“…These authors use free counterterms in the space between the plates and place additional surface counterterms at the boundaries. Later on various authors proposed the use of exactly the same renormalization procedure for various physical problems [24]. The first calculation for the NLO of Casimir energy for the massive scalar field using this renormalization program is done in Ref.…”

Section: Introductionmentioning

confidence: 99%

A new renormalization approach to the Dirichlet Casimir effect for ϕ4 theory in 1+1 dimensions

Moazzemi¹,

Gousheh²

2008

Physics Letters B

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The next to the leading order Casimir effect for a real scalar field, within φ 4 theory, confined between two parallel plates is calculated in one spatial dimension. Here we use the Green's function with the Dirichlet boundary condition on both walls. 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. We obtain finite results for the massive and massless cases, in sharp contrast to some of the other reported results. Secondly, and probably less importantly, we use a supplementary renormalization procedure in addition to the usual regularization and renormalization programs, which makes the usage of any analytic continuation techniques unnecessary.

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“…These authors use free counterterms in the space between the plates and place additional surface counterterms at the boundaries. Later on various authors proposed the use of exactly the same renormalization procedure for various physical problems [20]. The first calculation for the NLO of Casimir energy for the massive scalar field using this renormalization program is done in ref.…”

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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Boundary conditions as mass generation mechanism for real scalar fields

Cited by 9 publications

References 27 publications

Radiative correction to the Casimir energy for massive scalar field on a spherical surface

Radiative correction to the Casimir energy for massive scalar field on a spherical surface

A new renormalization approach to the Dirichlet Casimir effect for ϕ4 theory in 1+1 dimensions

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

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Boundary conditions as mass generation mechanism for real scalar fields

Cited by 9 publications

References 27 publications

Radiative correction to the Casimir energy for massive scalar field on a spherical surface

Radiative correction to the Casimir energy for massive scalar field on a spherical surface

A new renormalization approach to the Dirichlet Casimir effect for ϕ4 theory in 1+1 dimensions

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

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Product

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