The Casimir energy for scalar field with mixed boundary condition

Valuyan, M. A.

doi:10.1142/s0219887818501724

Cited by 8 publications

(3 citation statements)

References 20 publications

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“…which is perfectly consistent with the previously reported result without a Lifshitz critical exponent [40].…”

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confidence: 94%

One-Loop Correction to The Casimir Energy in Lifshitz-Like Theory

Valuyan

2021

Preprint

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In the present article, Radiative Correction 1 (RC) to the Casimir energy was computed for the self-2 interacting massive / massless Lifshitz-like scalar field, 3 confined between a pair of plates with Dirichlet and 4 Mixed boundary conditions in 3 + 1 dimensions. More-5 over, using the results obtained for the Dirichlet Casimir 6 energy, the RC to the Casimir energy for Periodic and 7 Neumann boundary conditions were also draw outed. 8 To renormalize the bare parameters of the Lagrangian, 9 a systematic perturbation expansion was used in which 10 the counterterms were automatically obtained in a po-11 sition -dependent manner. In our view, the position 12 dependency of the counterterm was allowed, since it re-13 flected the effects of the boundary condition imposed or 14 the background space in the problem. All the answers 15 obtained for the Casimir energy were consistent with 16 well-known physical expects. In a language of graphs, 17 the Casimir energy for the massive Lifshitz-like scalar 18 field confined with four boundary conditions (Dirichlet, 19 Neumann, Mixed, and Periodic) was also compared to 20 each other, and as a concluding remark, the sign and 21 magnitude of their values were discussed.

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“…which is perfectly consistent with the previously reported result without a Lifshitz critical exponent [40].…”

supporting

confidence: 94%

One-Loop Correction to The Casimir Energy in Lifshitz-Like Theory

Valuyan

2021

Preprint

Self Cite

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“…Various methods for renormalization and regularization have been devised to facilitate accurate calculations in this domain. These methods encompass the Zeta function regularization technique, [27][28][29], Heat kernel series, [30], and Green's function method, [31,32]. In this regard, comprehensive investigations have been undertaken to delve into radiative corrections to the Casimir energy across various fields and geometries [7,33].…”

Section: Introductionmentioning

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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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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“…Dealing with divergent expressions makes an important part of calculating the Casimir energy. Therefore, to regularize the divergent expressions, different types of regularization technique were introduced [38,39,40,41,42,43,44,45,46,47]. In this study, to regularize and remove infinities caused by the vacuum energies, Box Subtraction Scheme (BSS), as a regularization technique were employed.…”

Section: Introductionmentioning

confidence: 99%

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

Valuyan

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

The Casimir energy for scalar field with mixed boundary condition

Cited by 8 publications

References 20 publications

One-Loop Correction to The Casimir Energy in Lifshitz-Like Theory

One-Loop Correction to The Casimir Energy in Lifshitz-Like Theory

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

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