  A new approach to generalised Casimir type of problems is derived within the
context of renormalisable quantum field theory (QFT). We study the simplest
case of a massive fluctuating boson field coupled to a time-independent
background potential. We use analytic properties of scattering data to compute
the relevant Green's functions at imaginary momenta, which in turn yields a
simple and efficient method to compute (one-loop) vacuum energy densities in
QFT. Renormalisation is easily performed in the perturbative sector by
identifying low order Feynman diagrams with the first few Born approximation to
the Green's function. Numerical examples illustrate the efficiency of our
approach.
