Lattice QCD has made significant progress in determining
the properties of resonances which decay predominantly into
two-particle channels. This work uses a method, initially developed
by Martin Luscher, in which the spectrum of two-particle states
in a finite spatial box of varying size is related to the infinite volume
scattering amplitudes. However, many resonances decay also to three-particle
channels, and thus a generalization of the theoretical framework is
needed. Such a framework exists only in special cases, e.g. in the
non-relativistic domain close to threshold. I present a generalization
of Luscher's method that applies for three identical relativistic particles, connecting the finite-volume spectrum to infinite-volume
scattering quantities. I sketch how this method might be used in
practice, and note its successes and shortcomings.
This is based on work with Max Hansen.