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We examine the Casimir energy of 5D electro-magnetism in the recentstandpoint. Z$_2$ symmetry is taken into account. After confirming theconsistency with the past result, we do new things based on a newregularization. The regularization is based on the minimal area principle andthe regularized configuration is the {\it sphere lattice}. We do it not in theKaluza-Klein expanded form but in the closed form. The formalism is based onthe heat-kernel approach using the position/momentum propagator. A usefulexpression of the Casimir energy, in terms of the P/M propagator, is obtained.Renormalization flow is realized as the change along the extra-axis.

Casimir and Vacuum Energy of 5D Warped System and Sphere Lattice Regularization