Revisiting Vacuum Energy in Compact Spacetimes

Abstract

We revisit the calculation of vacuum energy density in compact spacetimes. By explicitly computing the effective action through the heat kernel method, we compute vacuum energy density for the general case of k compact spatial dimensions in p+k dimensional Minkowski spacetime. Additionally, we use this formalism to calculate the Casimir force on a piston placed in such spacetimes, and note the deviations from previously reported results in the literature.