Two-particle wave function in four dimensional Ising model

TL;DR

This paper investigates the two-particle wave functions in a four-dimensional Ising model, calculating ground, excited, and unstable states, and deriving scattering phase shifts using a diagonalization method.

Contribution

It introduces a method to compute two-particle wave functions and scattering phase shifts in a four-dimensional lattice model, including unstable states.

Findings

Wave functions for various states are successfully calculated.

Scattering phase shifts are derived from the wave functions.

The study demonstrates the applicability of the diagonalization method in higher dimensions.

Abstract

An exploratory study of two-particle wave function is carried out with a four dimensional simple model. The wave functions not only for two-particle ground and first excited states but also for an unstable state are calculated from three- and four-point functions using the diagonalization method suggested by L\"uscher and Wolff. The scattering phase shift is evaluated from these wave functions.