Vacuum Energy for Generalized Dirac Combs at T = 0

Abstract

The quantum vacuum energy for a hybrid comb of Dirac δ-δ′ potentials is computed by using the energy of the single δ-δ′ potential over the real line that makes up the comb. The zeta function of a comb periodic potential is the continuous sum of zeta functions over the dual primitive cell of Bloch quasi-momenta. The result obtained for the quantum vacuum energy is non-perturbative in the sense that the energy function is not analytical for small couplings.