Towards a nonperturbative construction of the $S$-matrix

TL;DR

This paper introduces a nonperturbative method for calculating the $S$-matrix in strongly-coupled quantum field theories using spectral data from Hamiltonian methods, demonstrated on the 2+1d $O(N)$ model.

Contribution

It provides a novel nonperturbative recipe for $S$-matrix computation applicable to strongly-coupled theories, including QCD, using Hamiltonian spectral data.

Findings

Successfully computed the 2→2 scattering amplitude in the 2+1d $O(N)$ model.

Reproduced the full scattering amplitude for arbitrary complex energies.

Demonstrated the method's potential for theories like QCD.

Abstract

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