Towards a nonperturbative construction of the S-matrix

We present a nonperturbative recipe for directly computing the $S$-matrix in strongly-coupled QFTs. The method makes use of spectral data obtained Hamiltonian framework and can be applied to wide range theories, including potentially QCD. demonstrate utility this prescription specific example 2+1d $O(N)$ model at large $N$, using energy eigenstates computed with truncation reproduce full $2 \to 2$ scattering amplitude arbitrary (complex) center-of-mass energy.