Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position / momentum propagator is exploited. A new regularization, called sphere lattice regularization, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do not take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its Λ(4D UV-cutoff), ω(5D bulk curvature, warpedness parameter) and T(extra space IR parameter) dependence. Casimir energy is the free part of the vacuum energy. It depends only on the macro (boundary) parameters. It is the macroscopic quantum effect. In the recent strong interest in the brane models or the bulk-boundary theories, the subject is quite important. The higher dimensional Casimir energy was examined by Appelquist and Chodos1. They considered the flat geometry of S1 × M4. It has been, in the recent standpoint, re-examined 2. Here we examine the warped case. In the closed form, ECas of 5D electro-magnetism is expressed as ECas(ω, T) = Cas (ω, T) = ∫ d 4
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