On a possible method of Casimir pressure renormalization in a ball

Dubikovsky, A. I.; Silaev, P. K.; Timofeevskaya, O. D.

doi:10.1142/s0217732315500674

Cited by 5 publications

(4 citation statements)

References 31 publications

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“…The selection of an appropriate counterterm has been a subject of extensive debate within the literature [37]. In the majority of prior studies, the free counterterm, designed for Minkowski space, has been utilized in renormalization programs [42][43][44]. Nevertheless, the importance of adopting a counterterm that is in line with the boundary conditions imposed was underscored in the discussions presented in Refs.…”

Section: The Modelmentioning

confidence: 99%

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Radiative correction to the Casimir energy for Lorentz-violating scalar field in d + 1 dimensions

Valuyan

2020

Mod. Phys. Lett. A

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The renormalization program in every renormalized theory should run consistently with the type of boundary condition imposed on quantum fields. To maintain this consistency, the counterterms usually appear in the position-dependent form. In this study, using such counterterms, we calculated the radiative correction to the Casimir energy for massive and massless Lorentz-violating scalar field constrained with Dirichlet boundary condition between two parallel plates in [Formula: see text] spatial dimensions. In the calculation procedure, to remove infinities appearing in the vacuum energies, the box subtraction scheme (BSS) supplemented by the cutoff regularization technique and analytic continuation technique was employed. Normally, in the BSS, two similar configurations are defined and their vacuum energies are subtracted from each other in the appropriate limits. Our final results regarding all spatial dimensions were convergent and consistent with the expected physical basis. We further plotted the Casimir energy density for the time-like and space-like Lorentz-violating systems in a number of odd and even dimensions; multiple aspects of the obtained results were ultimately discussed.

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Section: The Modelmentioning

confidence: 99%

“…(2) serves as a clear demonstration of the consistency between the outcomes derived in Eqs. ( 43) and (44). Within this figure, the thermal correction to the Casimir energy for both massive and massless scalar fields has been graphically represented.…”

Section: B the Case Of Lv1 And Lv2 Lorentz Violationsmentioning

confidence: 99%

Radiative correction to the Casimir energy for Lorentz-violating scalar field in d + 1 dimensions

Valuyan

2020

Mod. Phys. Lett. A

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“…Typically, the use of counterterms in the renormalization program is to eliminate divergences caused by the bare parameters of Lagrangian (e.g., the bare mass of the quantum field and bare coupling constant). In most of the previous works, the free counterterm (used for Minkowski space) was applied in renormalization programs [18,25,26,27,28]. Additionally, in some articles, the influence of imposed boundary conditions was added in counterterms [29].…”

Section: Introductionmentioning

confidence: 99%

Radiative Correction to the Casimir Energy for Lorentz-violating Scalar Field in d+1 Dimensions

Valuyan

2020

Preprint

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The renormalization program in every renormalized theory should be run consistently with the type of boundary condition imposed on quantum fields. To maintain this consistency, the counterterms usually appear in the position-dependent form. In the present study, using such counterterms, we calculated the radiative correction to the Casimir energy for massive and massless Lorentzviolating scalar field constrained with Dirichlet boundary condition between two parallel plates in d spatial dimensions. In the calculation procedure, to remove infinities appearing in the vacuum energies, the box subtraction scheme supplemented by the cutoff regularization technique and analytic continuation technique were employed. Normally, in the box subtraction scheme, two similar configurations are defined and their vacuum energies are subtracted from each other in the appropriate limits. Our final results regarding all spatial dimensions were convergent and consistent with the expected physical basis. We further plotted the Casimir energy density for the time-like and space-like Lorentz-violating systems in a number of odd and even dimensions; multiple aspects of the obtained results were ultimately discussed.

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“…An alternative solution to this problem is possible in the limit of a small perturbation, when the relative permittivity is close to unity [24][25][26][27]. Another method of choosing the normalization point for the Casimir energy in a ball allowing to solve the problem of a dielectric ball (this method does not rely on the problem of an infinitely thin conducting sphere) was proposed in [28,29].…”

Section: Introductionmentioning

confidence: 99%

On the Possibility of the Implicit Renormalization of the Casimir Energy

Dubikovsky

Silaev

2018

Moscow Univ. Phys.

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We propose a procedure for the renormalization of Casimir energy, that is based on the implicit versions of standard steps of renormalization procedure -regularization, subtraction and removing the regularization. The proposed procedure is based on the calculation of a set of convergent sums, which are related to the original divergent sum for the nonrenormalized Casimir energy. Then one constructs a linear equations system, that connects this set of convergent sums with the renormalized Casimir energy, which is a solution to this equations system. This procedure slightly reduces the indeterminancy that arises in standard procedure when we choose the particular regularization and the explicit form of counterterm. The proposed procedure is more efficient from the computational point of view than the standard one. It can be applied not only for systems with the explicit transcendental equation for the spectrum, but also for systems with the spectrum that can be obtained only numerically.Keywords: quantized fields, vacuum of quantum field theory, zero-point oscillations, Casimir effect.

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On a possible method of Casimir pressure renormalization in a ball

Cited by 5 publications

References 31 publications

Radiative correction to the Casimir energy for Lorentz-violating scalar field in d + 1 dimensions

Radiative correction to the Casimir energy for Lorentz-violating scalar field in d + 1 dimensions

Radiative Correction to the Casimir Energy for Lorentz-violating Scalar Field in d+1 Dimensions

On the Possibility of the Implicit Renormalization of the Casimir Energy

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