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

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.