Casimir Energy of AdS5 Electromagnetism and Cosmological Constant Problem

Casimir energy is calculated for the 5D electromagnetism in the warped geometry. It is compared with the flat case(arXiv:0801.3064). A new regularization, called sphere lattice regularization, is taken. It is based on the minimal area principle and is a direct realization of the geometrical approach to the renormalization group. The properly regularized form of Casimir energy, is expressed in a closed form. We numerically evaluate Λ(4D UV-cutoff), ω(5D bulk curvature, warp parameter) and T (extra space IR parameter) dependence of the Casimir energy. The warp parameter ω suffers from the renormalization effect. We examine the meaning of the weight function and finally reach a new definition of the Casimir energy where the 4D momenta( or coordinates) are quantized with the extra coordinate as the Euclidean time. We comment on the cosmological term at the end.