Lattice QCD is the only known systematic method for calculating
non-perturbative matrix elements in QCD, the theory of the strong
interactions. However, there is currently no known method for
extracting scattering and decay amplitudes involving more than two
hadrons. The most promising approach, already developed by Martin
Luescher for the two-particle case, is to extract amplitudes from
the finite-volume spectrum. We present work towards generalizing
Luescher's relation between finite-volume spectrum and S-matrix
to include three-particle states.