Orientation-Dependent Casimir Energy and Generalized Torque in Lorentz-Violating Rectangular Compactifications
Abstract
We derive the renormalized Casimir energy of a free massive real scalar field on the rectangular compactification ℝ1,r× Tp in the presence of a constant CPT-even aether-like Lorentz-violating background. Allowing the spatial part of the background vector to have an arbitrary orientation relative to the compactification lattice, we characterize the resulting orientation-dependent geometric response of the vacuum. Integrating out the noncompact momenta reduces the effective spatial kinetic matrix to its Schur complement, and Poisson resummation yields a closed, exponentially convergent Bessel-function lattice sum within the stability domain. The resulting expression separates an orientation-independent kinetic normalization, [1+λuμuμ]−1/2, from an orientation-dependent deformation of the image-lattice metric. Coordinate-aligned configurations are recovered as special cases, and the exact massless limit and the compact-direction pressures are obtained. For a two-dimensional compact subspace, we explicitly analyze the angular dependence of the vacuum energy and derive the associated generalized Casimir torque. These results establish how the relative orientation between a Lorentz-violating background and an anisotropic compactification lattice enters the renormalized vacuum energy and its directional response.
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BibTeX
@misc{gofreh2026orientationdependent,
title = {{Orientation-Dependent Casimir Energy and Generalized Torque in Lorentz-Violating Rectangular Compactifications}},
author = {Zohreh Ashkipoor Gofreh and Reza Moazzemi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20745},
eprint = {2610.20745},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20745},
}
RIS
TY - UNPB
TI - Orientation-Dependent Casimir Energy and Generalized Torque in Lorentz-Violating Rectangular Compactifications
AU - Zohreh Ashkipoor Gofreh
AU - Reza Moazzemi
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20745
UR - https://arxiv.org/abs/2610.20745
AB - We derive the renormalized Casimir energy of a free massive real scalar field on the rectangular compactification ℝ^1,r× T^p in the presence of a constant CPT-even aether-like Lorentz-violating background. Allowing the spatial part of the background vector to have an arbitrary orientation relative to the compactification lattice, we characterize the resulting orientation-dependent geometric response of the vacuum. Integrating out the noncompact momenta reduces the effective spatial kinetic matrix to its Schur complement, and Poisson resummation yields a closed, exponentially convergent Bessel-function lattice sum within the stability domain. The resulting expression separates an orientation-independent kinetic normalization, [1+λu_μu^μ]^−1/2, from an orientation-dependent deformation of the image-lattice metric. Coordinate-aligned configurations are recovered as special cases, and the exact massless limit and the compact-direction pressures are obtained. For a two-dimensional compact subspace, we explicitly analyze the angular dependence of the vacuum energy and derive the associated generalized Casimir torque. These results establish how the relative orientation between a Lorentz-violating background and an anisotropic compactification lattice enters the renormalized vacuum energy and its directional response.
ER -