- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Nonperturbative corrections to the Casimir energy for a scalar field theory with nonlinear boundary conditions

Fabrizio Canfora1,2,*, David Dudal3,†, Thomas Oosthuyse3,‡, Pablo Pais4,5,§, Luigi Rosa6,7,∥, and Sebbe Stouten3,¶

  • *Contact author: fabrizio.canfora@uss.cl
  • †Contact author: david.dudal@kuleuven.be
  • ‡Contact author: thomas.oosthuyse@kuleuven.be
  • §Contact author: pais@ipnp.troja.mff.cuni.cz
  • ∥Contact author: rosa@na.infn.it
  • Contact author: sebbe.stouten@kuleuven.be
PDF

Phys. Rev. D 113, 114033 – Published 17 June, 2026

DOI: https://doi.org/10.1103/kr43-21n3

Abstract

We consider the case of a free real massive bulk scalar in D=4 dimensions, and embed two parallel plates as interfaces on which we impose nonlinear boundary conditions, either Dirichlet- or Neumann-like, parametrized by a new coupling constant g. The system mimics a non-Abelian gauge theory supplemented with boundary conditions on surfaces embedded in the bulk. We present the first evidence for a nonperturbative 1g2 boundary mass generation and its ensuing correction to the standard Casimir energy. This result becomes possible by incorporating dynamical corrections to the effective boundary fields, which are used to build in the boundary conditions directly at the action level.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. G. Plunien, B. Muller, and W. Greiner, Phys. Rep. 134, 87 (1986).
  2. M. Bordag, U. Mohideen, and V. M. Mostepanenko, Phys. Rep. 353, 1 (2001).
  3. K. A. Milton, J. Phys. A 37, R209 (2004).
  4. M. Bordag, G. Klimchitskaya, U. Mohideen, and V. M. Mostepananko, Advances in the Casimir Effect, Vol. 145 (Oxford University Press, 2009).
  5. H. B. G. Casimir, Indagat. Math 10, 261 (1948).
  6. M. N. Chernodub, V. A. Goy, A. V. Molochkov, and H. H. Nguyen, Phys. Rev. Lett. 121, 191601 (2018).
  7. M. N. Chernodub, V. A. Goy, A. V. Molochkov, and A. S. Tanashkin, Phys. Rev. D 108, 014515 (2023).
  8. B. A. Ngwenya, The Casimir effect in non-Abelian gauge theories on the lattice, Other thesis, 2025, arXiv:2505.02875.
  9. B. A. Ngwenya, A. K. Rothkopf, and W. A. Horowitz, arXiv:2507.21333.
  10. A. Athenodorou and M. Teper, J. High Energy Phys. 11 (2020) 172.
  11. M. N. Chernodub, V. A. Goy, A. V. Molochkov, and A. S. Tanashkin, Phys. Rev. D 113, 034512 (2026).
  12. D. Dudal, P. De Fabritiis, and S. Stouten, J. High Energy Phys. 01 (2026) 087.
  13. D. Karabali, A. Maj, and V. P. Nair, Phys. Rev. D 112, 094037 (2025).
  14. A. A. Saharian and H. H. Asatryan, Eur. Phys. J. Plus 141, 106 (2026).
  15. D. Karabali and V. P. Nair, Nucl. Phys. B464, 135 (1996).
  16. D. Karabali and V. P. Nair, Phys. Rev. D 98, 105009 (2018).
  17. G. Curci and R. Ferrari, Nuovo Cimento A 32, 151 (1976).
  18. M. Peláez, U. Reinosa, J. Serreau, M. Tissier, and N. Wschebor, Rep. Prog. Phys. 84, 124202 (2021).
  19. M. Bordag, D. Robaschik, and E. Wieczorek, Ann. Phys. (N.Y.) 165, 192 (1985).
  20. R. Golestanian and M. Kardar, Phys. Rev. A 58, 1713 (1998).
  21. D. Dudal, P. Pais, and L. Rosa, Phys. Rev. D 102, 016026 (2020).
  22. F. Canfora, D. Dudal, T. Oosthuyse, P. Pais, and L. Rosa, J. High Energy Phys. 09 (2022) 095.
  23. T. Oosthuyse and D. Dudal, SciPost Phys. 15, 213 (2023).
  24. F. Canfora, D. Dudal, T. Oosthuyse, L. Rosa, and S. Stouten, J. High Energy Phys. 03 (2024) 161.
  25. D. Dudal, A. Gobeyn, T. Oosthuyse, S. Stouten, and D. Vercauteren, Phys. Rev. D 110, 065015 (2024).
  26. D. Dudal, T. Oosthuyse, S. Stouten, A. Gobeyn, and B. W. Mintz, Ann. Phys. (Amsterdam) 470, 169827 (2024).
  27. S. Giombi and H. Khanchandani, J. High Energy Phys. 08 (2019) 010.
  28. N. Andrei et al., J. Phys. A 53, 453002 (2020).
  29. I. M. Gel’fand and A. M. Yaglom, J. Math. Phys. (N.Y.) 1, 48 (1960).
  30. G. V. Dunne, J. Phys. A 41, 304006 (2008).
  31. J. Ambjorn and S. Wolfram, Ann. Phys. (N.Y.) 147, 1 (1983).
  32. E. Kashani, A. Mohebbi, A. E. Feili Monfared, and A. Raoof, Chem. Eng. Sci. 247, 116925 (2022).
  33. G. S. Agarwal and S. D. Gupta, Opt. Lett. 12, 829 (1987).
  34. B. Painter, G. Ferrari, and M. Amabili, Nonlinear Dyn. 108, 2903 (2022).

Outline

Information

Phys. Rev. D 113, 114033– Published 17 June, 2026
  • Received 11 December 2025
  • Accepted 6 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation