On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy-momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form gμ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p⩽0.