The one-loop Casimir energy for a Lorentz-violating scalar field between rough membranes is claimed to equal the smooth-plate result at a rescaled separation, but the periodic-boundary sector is off by a factor of eight.
Furthermore, for DBC/NBC, the domain of nB is nD, N ∈ N, while for the case of MBC, the domain is nM ∈ N ∪ {0}
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One-Loop Correction to the Casimir Energy in Lorentz-Violating $\phi^4$ Theory with Rough Membrane Boundaries
The one-loop Casimir energy for a Lorentz-violating scalar field between rough membranes is claimed to equal the smooth-plate result at a rescaled separation, but the periodic-boundary sector is off by a factor of eight.