Towards a nonperturbative construction of the S-matrix

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 → 2 scattering amplitude for arbitrary (complex) center-of-mass energy.

Effective Hamiltonians and Counterterms for Hamiltonian Truncation

“…See for example refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], as well as the reviews [26,27]. A particularly important focus for research in this area has been on the development of effective Hamiltonians for improving the accuracy of Hamiltonian Truncation estimates [4,[28][29][30][31][32][33][34].…”