Probing Lorentz symmetry violation via the Casimir effect in rectangular cavities

Abstract

We investigate the Casimir effect as a probe of Lorentz symmetry violation for a real scalar field confined to a rectangular waveguide with Dirichlet boundary conditions. The field dynamics is governed by a Lorentz-violating extension of the Klein-Gordon theory involving a fixed background four-vector $u_μ$. Focusing on four representative configurations in which the background is aligned with the temporal direction or with one of the spatial axes of the cavity, we derive the modified mode spectra and the corresponding vacuum energies. We show that these configurations induce anisotropic modifications of the dispersion relations that depend explicitly on the orientation of the background vector relative to the cavity geometry, while still preserving mode separability. The resulting Casimir energy acquires characteristic direction-dependent corrections that encode the breaking of Lorentz symmetry, without altering the universal functional structure of the spectral kernel. Our analysis provides a controlled and transparent framework for isolating Lorentz-violating effects in confined geometries and highlights Casimir systems as sensitive probes of anisotropic physics and fundamental spacetime symmetries.

Figures (9)

• Figure 1: Rectangular cavity formed by parallel plates located at $x=0, \ L_x$ and $y=0, \ L_y$, confining a massive scalar field $\phi(x,y,z)$ with Dirichlet boundary conditions. The field is free along the $z$-direction, which is taken to be unbounded.
• Figure 2: Dimensionless Casimir energy density $8 \pi^2 \mathcal{E}_C^{(I)}/\hbar c \mu^3$ for Case I as a function of the plate separation distances $L_x\mu$ and $L_y\mu$ for different Lorentz-violating parameters $\Lambda = \{0.0, 0.1, 0.2, 0.3\}$. The left panel shows the 1D energy profile for a fixed $L_y\mu = 1.0$, highlighting the attenuation of the vacuum energy as $\Lambda$ increases. The right panel displays the 3D overlapping energy surfaces, providing a global perspective of the energy decay.
• Figure 3: Contour maps of the Casimir energy density for Case I, considering four distinct values of the LV parameter: $\Lambda = 0.0$ (standard Case), $0.1, 0.2$ and $0.3$. The color gradient and the superimposed iso-energy lines represent the magnitude of $8 \pi^2 \mathcal{E}_C^{(I)}/\hbar c \mu^3$. The perfect symmetry of the concentric contours across all panels demonstrates that Case I preserves spatial isotropy in the $L_x$-$L_y$ plane, while the LV parameter acts as a global scaling factor for the energy intensity.
• Figure 4: Dimensionless Casimir energy density $8 \pi^2 \mathcal{E}_C^{(II)}/\hbar c \mu^3$ for Case II as a function of the plate separation distances $L_x\mu$ and $L_y\mu$ for different Lorentz-violating parameters $\Lambda = \{0.0, 0.1, 0.2, 0.3\}$. The left panel shows the 1D energy profile for a fixed $L_y\mu = 1.0$, highlighting the anisotropic attenuation of the vacuum energy magnitude as $\Lambda$ increases. The right panel displays the 3D overlapping energy surfaces, providing a global perspective of the energy decay and the geometric deformation induced by the spatial Lorentz-violating component $u_1$.
• Figure 5: Contour maps of the Casimir energy density for Case II, considering four distinct values of the LV parameter: $\Lambda = 0.0$ (standard Case), $0.1, 0.2,$ and $0.3$. The color gradient and the superimposed iso-energy lines represent the magnitude of $8 \pi^2 \mathcal{E}_C^{(II)}/\hbar c \mu^3$. The progressive elongation of the contours along the $L_x \mu$ axis demonstrates that Case II breaks spatial isotropy in the $L_x$-$L_y$ plane, as the LV parameter introduces a directional deformation in the effective confinement scale.