Lattice QCD calculations have made great strides towards calculating resonance properties and decay amplitudes in cases where only two-particle channels are present. This required development of both theoretical formalism and simulation methods. However, many problems of interest involve three-particle channels, e.g. the Roper resonance and K -> 3 pion decays, and for these the theoretical formalism to relate the finite-volume lattice results to infinite-volume scattering quantities has been lacking.
After reviewing methods and results involving two particles, I describe recent work with Raúl Briceño and Max Hansen in which we have developed the needed formalism in a generic relativistic field theory of identical scalar particles, and present results from a numerical implementation of the formalism in the isotropic approximation.
I close with a brief discussion of ongoing work with Tyler Blanton and Fernando Romero-López in which we go beyond the isotropic approximation and include d-wave interactions.