Quantum corrections to the Casimir effect in a scalar Hořava-Lifshitz theory with rough plates at low temperature
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Bórquez, Claudio, Droguett, Byron
Institutions: Universidad San Sebastián, Universidad de Antofagasta
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215073067