Casimir energy per area E(a) = -pi^2 hbar c / (720 a^3); zeta(-1) = -1/12

Casimir-force framework via zeta-function regularisation (Casimir 1948 Proc K Ned Akad Wet 51, 793). Setup: two parallel conducting plates area A separation a in vacuum admit EM modes with lambda_n = 2a/n (n = 1, 2, ...). Zero-point energy…