Quantum corrections to the Casimir effect in a scalar Hořava-Lifshitz theory with rough plates at low temperature
Abstract
We investigate the Casimir effect of a massive, self-interacting real scalar field with quartic coupling in a (3+1)-dimensional Hořava-Lifshitz-type theory, subject to rough boundaries obeying Dirichlet boundary conditions. Using the effective action and generalized ζ-function approach, we derive the renormalized effective potential, incorporating anisotropic scaling, boundary roughness, and temperature in the low-temperature regime. We determine the topological mass at one-loop order and the Casimir energy up to two loops. In the massless limit, the topological mass and the two-loop Casimir contribution exhibit infrared divergences for odd values z>1, associated with the absence of an intrinsic mass scale, while the one-loop Casimir energy remains finite. For z=1, the standard relativistic Dirichlet result is recovered in the zero-temperature and vanishing-roughness limits.
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BibTeX
@misc{borquez2026quantum,
title = {{Quantum corrections to the Casimir effect in a scalar Hořava-Lifshitz theory with rough plates at low temperature}},
author = {Claudio Bórquez and Byron Droguett},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40081},
eprint = {2609.40081},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40081},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum corrections to the Casimir effect in a scalar Hořava-Lifshitz theory with rough plates at low temperature
AU - Claudio Bórquez
AU - Byron Droguett
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40081
UR - https://arxiv.org/abs/2609.40081
AB - We investigate the Casimir effect of a massive, self-interacting real scalar field with quartic coupling in a (3+1)-dimensional Hořava-Lifshitz-type theory, subject to rough boundaries obeying Dirichlet boundary conditions. Using the effective action and generalized ζ-function approach, we derive the renormalized effective potential, incorporating anisotropic scaling, boundary roughness, and temperature in the low-temperature regime. We determine the topological mass at one-loop order and the Casimir energy up to two loops. In the massless limit, the topological mass and the two-loop Casimir contribution exhibit infrared divergences for odd values z>1, associated with the absence of an intrinsic mass scale, while the one-loop Casimir energy remains finite. For z=1, the standard relativistic Dirichlet result is recovered in the zero-temperature and vanishing-roughness limits.
ER -