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Casimir energy for the interaction of -plates with a massless real scalar field.

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Title: Casimir energy for the interaction of -plates with a massless real scalar field.
Authors: Kraskov, M. V.1 (AUTHOR) misakraskov@mail.ru, Pis'mak, Yu. M.1 (AUTHOR) y.pismak@spbu.ru
Source: Theoretical & Mathematical Physics. Jun2026, Vol. 227 Issue 3, p1026-1037. 12p.
Subjects: Scalar field theory, Functional integration, Potential theory (Mathematics), Matrices (Mathematics), Vacuum energy (Astronomy), Boundary value problems, Chebyshev polynomials
Abstract: Within the Symanzik approach, we consider a massless real scalar field in Euclidean spacetime in the presence of planar -plates with an interaction potential. Using functional integration and the Sylvester identity, the interaction energy density (per unit area) can be reduced to the logarithm of the determinant of an matrix. After subtracting the self-energy contribution, the geometry of the system allows the problem to be reduced to calculating the determinant of a tridiagonal matrix, which is evaluated using a recurrence relation. For a system of identical plates with equal separations, we obtain a closed expression in terms of Chebyshev polynomials. As an illustration of the efficiency of the method, an explicit form for is written out, and the limiting case of infinitely strong interaction (), which is associated with Dirichlet boundary conditions, is considered. In addition, we show that in the case where the number of plates and the separation , at fixed thickness and with weak coupling constant , the system of -films approaches a finite-thickness slab. The results are verified for the particular cases and. [ABSTRACT FROM AUTHOR]
Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Casimir energy for the interaction of -plates with a massless real scalar field.
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  Data: <searchLink fieldCode="AR" term="%22Kraskov%2C+M%2E+V%2E%22">Kraskov, M. V.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> misakraskov@mail.ru</i><br /><searchLink fieldCode="AR" term="%22Pis'mak%2C+Yu%2E+M%2E%22">Pis'mak, Yu. M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> y.pismak@spbu.ru</i>
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  Data: <searchLink fieldCode="JN" term="%22Theoretical+%26+Mathematical+Physics%22">Theoretical & Mathematical Physics</searchLink>. Jun2026, Vol. 227 Issue 3, p1026-1037. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Scalar+field+theory%22">Scalar field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+integration%22">Functional integration</searchLink><br /><searchLink fieldCode="DE" term="%22Potential+theory+%28Mathematics%29%22">Potential theory (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Vacuum+energy+%28Astronomy%29%22">Vacuum energy (Astronomy)</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Chebyshev+polynomials%22">Chebyshev polynomials</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Within the Symanzik approach, we consider a massless real scalar field in Euclidean spacetime in the presence of planar -plates with an interaction potential. Using functional integration and the Sylvester identity, the interaction energy density (per unit area) can be reduced to the logarithm of the determinant of an matrix. After subtracting the self-energy contribution, the geometry of the system allows the problem to be reduced to calculating the determinant of a tridiagonal matrix, which is evaluated using a recurrence relation. For a system of identical plates with equal separations, we obtain a closed expression in terms of Chebyshev polynomials. As an illustration of the efficiency of the method, an explicit form for is written out, and the limiting case of infinitely strong interaction (), which is associated with Dirichlet boundary conditions, is considered. In addition, we show that in the case where the number of plates and the separation , at fixed thickness and with weak coupling constant , the system of -films approaches a finite-thickness slab. The results are verified for the particular cases and. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1134/S0040577926060097
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Functional integration
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      – SubjectFull: Potential theory (Mathematics)
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      – SubjectFull: Matrices (Mathematics)
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      – SubjectFull: Boundary value problems
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              Text: Jun2026
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