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

Valuyan, M. A.

doi:10.1142/s0217732317501280

Cited by 8 publications

(3 citation statements)

References 55 publications

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“…On the other hand, by recalculating this quantity via the position-dependent counterterm, the answer was obtained convergent and consistent with all the expected physical basis [32]. Use of the position-dependent counterterms in the renormalization program even for problems defined in the curved space was also successful [36,37]. In a part of the present article, the Lorentz symmetry was violated.…”

Section: Introductionsupporting

confidence: 62%

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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Section: Introductionsupporting

confidence: 62%

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

Valuyan

2020

Preprint

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“…In fact, it can be interpreted that obtaining a position-dependent counterterms reflects the influence of BCs on the renormalization program. Later, this type of renormalization program has been used in multiple geometries defined in the flat and curved manifolds, and the achieved results for each case were physically consistent [18,20]. In this study, maintaining their idea and for the first time, we calculate the radiative correction to the Casimir energy between two points confined with the mixed BC in 1 + 1 dimensions.…”

Section: Introductionmentioning

confidence: 96%

The Casimir energy for scalar field with mixed boundary condition

Valuyan

2018

Int. J. Geom. Methods Mod. Phys.

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In the present study, the first-order radiative correction to the Casimir energy for massive and massless scalar fields confined with mixed boundary conditions (Dirichlet-Neumann) between two points in φ 4 theory was computed. Two issues in performing the calculations in this work are essential: to renormalize the bare parameters of the problem, a systematic method was employed, allowing all influences from the boundary conditions to be imported in all elements of the renormalization program. This idea yields our counterterms appeared in the renormalization program to be position-dependent. Using the Box Subtraction Scheme (BSS) as a regularization technique is the other noteworthy point in the calculation. In this scheme, by subtracting the vacuum energies of two similar configurations from each other, regularizing divergent expressions and their removal process were significantly facilitated. All the obtained answers for the Casimir energy with the mixed boundary condition were consistent with well-known physical grounds. We also compared the Casimir energy for massive scalar field confined with four types of boundary conditions (Dirichlet, Neumann, mixed of them and Periodic) in 1 + 1 dimensions with each other, and the sign and magnitude of their values were discussed.

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“…The BSS has been successful in presenting a physical answer for the Casimir energy problem designed in even spatial dimensions, which usually involves a high difficulty [20]. This scheme was also used for the calculation of the Casimir energy on a curved manifold and its result was consistent with known physical basis [21]. Moreover, BSS has been successfully implemented as a regularization technique supplementing by the aforementioned renormalization program in the calculation of higher order radiative correction to the Casimir energy [14].…”

Section: Figmentioning

confidence: 99%

The Dirichlet Casimir Energy for $ϕ^4$ Theory in a Rectangle

Valuyan

2018

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In this article, we present the zero and first-order radiative correction to the Dirichlet Casimir energy for massive and massless scalar field confined in a rectangle. This calculation procedure was conducted in two spatial dimensions and for the case of the first-order correction term is new. The renormalization program that we have used in this work, allows all influences from the dominant boundary conditions (e.g. the Dirichlet boundary condition) be automatically reflected in the counterterms. This permission usually makes the counterterms position-dependent. Along with the renormalization program, a supplementary regularization technique was performed in this work. In this regularization technique, that we have named Box Subtraction Scheme (BSS), two similar configurations were introduced and the zero point energies of these two configurations were subtracted from each other using appropriate limits. This regularization procedure makes the usage of any analytic continuation techniques unnecessary. In the present work, first, we briefly present calculation of the leading order Casimir energy for the massive scalar field in a rectangle via BSS. Next, the first order correction to the Casimir energy is calculated by applying the mentioned renormalization and regularization procedures. Finally, all the necessary limits of obtained answers for both massive and massless cases are discussed.

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

Cited by 8 publications

References 55 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

The Casimir energy for scalar field with mixed boundary condition

The Dirichlet Casimir Energy for $ϕ^4$ Theory in a Rectangle

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