Monte Carlo Calculation of Phase Shift in Four Dimensional O(4) $\phi^4$ Theory

TL;DR

This paper numerically computes the phase shift in four-dimensional O(4) $\

Contribution

It applies Lüscher's method to calculate phase shifts in $\

Findings

Results agree with perturbation theory predictions.

Identifies difficulties in extracting phase shifts at high momenta.

Highlights the need for precise energy level determination.

Abstract

The phase shift of the O(4) symmetric $\phi^4$ theory in the symmetric phase is calculated numerically using the relation between phase shift and energy levels of two-particle states recently derived by L\"{u}scher. The results agree with the prediction of perturbation theory. A practical difficulty of the method for a reliable extraction of the phase shift for large momenta due to the necessity of a precise determination of excited two-particle energy levels is pointed out.