Radiative Correction to The Casimir Energy For Scalar Field with Mixed Boundary Condition in 3 + 1 Dimensions

Document Type : Full length research Paper

Author

Department of Physics, Semnan Branch, Islamic Azad University, Semnan, Iran

Abstract

In the present study, the zero and first-order radiative correction to the Casimir energy for massive and massless scalar fields confined with mixed boundary conditions (Dirichlet-Neumann) between two parallel plates in ϕ^4 theory were computed. Two issues in performing the calculations in this work are essential: to renormalize the bare parameters of the problem, a systematic method were used, which 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 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 3+1 dimensions with each other, and the sign and magnitude of their values were discussed.

Keywords

References

 
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Journal of Research on Many-body Systems
Volume 9, Issue 3 - Serial Number 22
December 2019
Pages 187-201

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History

  • Receive Date: 18 December 2018
  • Revise Date: 08 June 2019
  • Accept Date: 07 July 2019

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