- 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

Casimir effect between semitransparent mirrors in a Lorentz-violating background

Román Linares1,*, C. A. Escobar1,†, A. Martín-Ruiz2,‡, and E. Plácido1,§

  • 1Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, 09340 Ciudad de México, México
  • 2Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México

  • *Contact author: lirr@xanum.uam.mx
  • †Contact author: carlos.escobar@xanum.uam.mx
  • ‡Contact author: alberto.martin@nucleares.unam.mx
  • §Contact author: lalo@xanum.uam.mx
PDF

Phys. Rev. D 112, 095041 – Published 24 November, 2025

DOI: https://doi.org/10.1103/lz5l-f6kd

Abstract

We investigate the Casimir effect for a massless scalar field confined between two parallel semitransparent mirrors in a vacuum modified by spontaneous Lorentz symmetry breaking. Using Green’s function techniques and a point-splitting evaluation of the stress-energy tensor, we compute the vacuum expectation value of the energy density T00. After a suitable renormalization, the Casimir energy is obtained as the difference between the vacuum configurations with and without the mirrors. We derive closed-form expressions that generalize the conventional result by simultaneously incorporating the mirror transparency and the Lorentz-violating background. Our analysis shows that the effect of transparency and Lorentz violation consists of a multiplicative correction and an effective rescaling of the plate separation, thereby modifying the functional dependence of the energy on the distance. Beyond the formal derivation, we discuss possible physical realizations of this framework, emphasizing anisotropic media such as nematic liquid crystals (e.g., 5CB), where uniaxial dielectric properties could emulate the Lorentz-violating background. Numerical estimates for such systems illustrate the phenomenological impact of our results and open the possibility of constraining Lorentz-violating coefficients through precision Casimir measurements.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. H. B. G. Casimir, On the attraction between two perfectly conducting plates, Proc. K. Ned. Akad. Wet. 51, 793 (1948), https://www.mit.edu/~kardar/research/seminars/Casimir/Casimir1948.pdf.
  2. M. J. Sparnaay, Measurements of attractive forces between flat plates, Physica (Utrecht) 24, 751 (1958).
  3. T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Casimir forces between arbitrary compact objects, Phys. Rev. Lett. 99, 170403 (2007).
  4. F. Chen, U. Mohideen, G. L. Klimchitskaya, and V. M. Mostepanenko, Demonstration of the lateral Casimir force, Phys. Rev. Lett. 88, 101801 (2002).
  5. S. Å. Ellingsen, I. Brevik, and K. A. Milton, Electrodynamic Casimir effect in a medium-filled wedge. II, Phys. Rev. E 80, 021125 (2009).
  6. A. W. Rodriguez, F. Capasso, and S. G. Johnson, The Casimir effect in microstructured geometries, Nat. Photonics 5, 211 (2011).
  7. B. A. Juárez-Aubry and R. Weder, Quantum field theory with dynamical boundary conditions and the Casimir effect: Coherent states, J. Phys. A 54, 105203 (2021).
  8. B. A. Juárez Aubry and R. Weder, A short review of the Casimir effect with emphasis on dynamical boundary conditions, Supl. Rev. Mex. Fís. 3, 020714 (2022).
  9. G. L. Klimchitskaya and V. M. Mostepanenko, Testing gravity and predictions beyond the standard model at short distances: The Casimir effect, in Modified and Quantum Gravity: From Theory to Experimental Searches on All Scales, edited by C. Pfeifer and C. Lämmerzahl (Springer International Publishing, Cham, 2023), pp. 403–445.
  10. L. Mattioli, A. M. Frassino, and O. Panella, Casimir-Polder interactions with massive photons: Implications for BSM physics, Phys. Rev. D 100, 116023 (2019).
  11. C. A. Escobar, E. Chan-López, and A. Martín-Ruiz, Casimir effect in polymer scalar field theory, Phys. Rev. D 101, 046023 (2020).
  12. D. Colladay and V. A. Kostelecký, CPT violation and the standard model, Phys. Rev. D 55, 6760 (1997).
  13. D. Colladay and V. A. Kostelecký, Lorentz-violating extension of the standard model, Phys. Rev. D 58, 116002 (1998).
  14. B. R. Edwards and V. A. Kostelecký, Riemann-Finsler geometry and Lorentz-violating scalar fields, Phys. Lett. B 786, 319 (2018).
  15. C. A. Escobar, L. Medel, and A. Martín-Ruiz, Casimir effect in Lorentz-violating scalar field theory: A local approach, Phys. Rev. D 101, 095011 (2020).
  16. C. A. Escobar, A. Martín-Ruiz, O. J. Franca, and M. A. G. García, A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation, Phys. Lett. B 807, 135567 (2020).
  17. A. Martín-Ruiz, C. A. Escobar, A. M. Escobar-Ruiz, and O. J. Franca, Lorentz violating scalar Casimir effect for a d-dimensional sphere, Phys. Rev. D 102, 015027 (2020).
  18. A. M. Escobar-Ruiz, A. Martín-Ruiz, C. A. Escobar, and R. Linares, Scalar Casimir effect for a conducting cylinder in a Lorentz-violating background, Int. J. Mod. Phys. A 36, 2150168 (2021).
  19. M. B. Cruz, E. R. B. de Mello, and A. Yu. Petrov, Fermionic Casimir effect in a field theory model with Lorentz symmetry violation, Phys. Rev. D 99, 085012 (2019).
  20. A. Rohim, A. Romadani, and A. S. Adam, Casimir effect of Lorentz-violating charged Dirac field in background magnetic field, Prog. Theor. Exp. Phys. 2024, 033B01 (2024).
  21. A. Martín-Ruiz and C. A. Escobar, Casimir effect between ponderable media as modeled by the standard model extension, Phys. Rev. D 94, 076010 (2016).
  22. A. Martín-Ruiz and C. A. Escobar, Local effects of the quantum vacuum in Lorentz-violating electrodynamics, Phys. Rev. D 95, 036011 (2017).
  23. F. Sorge, Casimir effect in a weak gravitational field, Classical Quantum Gravity 22, 5109 (2005).
  24. V. B. Bezerra, H. F. Mota, and C. R. Muniz, Thermal Casimir effect in closed cosmological models with a cosmic string, Phys. Rev. D 89, 024015 (2014).
  25. B. Nazari, Casimir effect of two conducting parallel plates in a general weak gravitational field, Eur. Phys. J. C 75, 501 (2015).
  26. C. A. Escobar, A. Martín-Ruiz, M. Mondragón, and R. Jáuregui, Gaussian beam propagation in a Lorentz-violating vacuum in the presence of a semi-transparent mirror, Phys. Scr. 98, 085527 (2023).
  27. L. H. C. Borges, A. F. Ferrari, and F. A. Barone, Mirrors and field sources in a Lorentz-violating scalar field theory, Nucl. Phys. B954, 114974 (2020).
  28. K A Milton, The Casimir Effect (World Scientific, Singapore, 2001).
  29. D. Deutsch and P. Candelas, Boundary effects in quantum field theory, Phys. Rev. D 20, 3063 (1979).
  30. Michael Edward Peskin and Daniel V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Addison-Wesley, Reading, MA, 1995), p. 842.
  31. L. S. Brown and G. J. Maclay, Vacuum stress between conducting plates: An image solution, Phys. Rev. 184, 1272 (1969).
  32. E. D. Palik, Handbook of Optical Constants of Solids: Volume 1 (Academic Press, New York, 2012).
  33. W. Gordon, Zur lichtfortpflanzung nach der relativitätstheorie, Ann. Phys. (Berlin) 377, 421 (1923).
  34. M. Visser, Acoustic black holes: Horizons, ergospheres and Hawking radiation, Classical Quantum Gravity 15, 1767 (1998).
  35. J. Li, S.-T. Wu, S. Brugioni, R. Meucci, and S. Faetti, Infrared refractive indices of liquid crystals, J. Appl. Phys. 97, 073501 (2005).
  36. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, International Series of Monographs on Physics (Clarendon Press, Oxford, 1993).
  37. A. Gómez, R. Martínez von Dossow, A. Martín-Ruiz, and L. F. Urrutia, Lorentz invariance violation and the CPT-odd electromagnetic response of a tilted anisotropic Weyl semimetal, Phys. Rev. D 109, 065005 (2024).
  38. R. Martínez von Dossow, A. Martín-Ruiz, and L. F. Urrutia, Higher-order derivative corrections to axion electrodynamics in 3D topological insulators, Symmetry 17, 581 (2025).

Outline

Information

Phys. Rev. D 112, 095041– Published 24 November, 2025
  • Received 28 September 2025
  • Accepted 9 November 2025
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