Strong Coupling Expansion for Scattering Phases in Hamiltonian Lattice Field Theories - I. the $(d+1)$-dimensional Ising model

TL;DR

This paper introduces a systematic strong coupling expansion method for calculating scattering phases in Hamiltonian lattice field theories, demonstrated on the $(d+1)$-dimensional Ising model, with potential applications to lattice gauge theories and QCD.

Contribution

The paper develops a convergent series method for scattering states and transition matrices in Hamiltonian lattice models, extending the analytical toolkit for non-perturbative studies.

Findings

Derived a convergent series for scattering states and transition matrices.

Computed next-to-leading order phase shifts in the Ising model.

Discussed applications to low-energy scattering in lattice gauge theories.

Abstract

A systematic method to obtain strong coupling expansions for scattering quantities in Hamiltonian lattice field theories is presented. I develop the conceptual ideas by means of the Hamiltonian field theory analogue of the Ising model, in $d$ space and one time dimension. The main result is a convergent series representation for the sacttering states and the transition matrix. To be explicit the special cases of $d=1$ and $d=3$ spatial dimensions are discussed in detail. I compute the next-to-leading order approximation for the phase shifts. The application of the method to investigate low-energy scattering phenomena in lattice gauge theory and QCD is proposed.