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

The phase shift of the O(4) symmetric ${\varphi }^4$ 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.