  We present a new approach to calculate the attractive long range
vortex-vortex interaction of the van der Waals type present in anisotropic and
layered superconductors. The mapping of the statistical mechanics of vortex
lines onto the imaginary time quantum mechanics of two dimensional charged
bosons allows us to define a 2D Casimir problem: Two half-spaces of (dilute)
vortex matter separated by a gap of width R are mapped to two dielectric
half-planes of charged bosons interacting via a massive gauge field. We
determine the attractive Casimir force between the two half-planes and show,
that it agrees with the pairwise summation of the van der Waals force between
vortices previously found by Blatter and Geshkenbein [Phys. Rev. Lett. 77, 4958
(1996)]
