Abstract
This calculation starts with the partial-wave dispersion relations for pion-pion scattering as deduced from the Mandelstam representation for the scattering amplitude. The contribution of the "left-hand cut" was calculated from $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ perturbation theory (to second order in $\ensuremath{\lambda}$). The $s$-wave and $p$-wave amplitudes were obtained numerically and found to agree closely with those obtained by Chew, Mandelstam, and Noyes who proceeded from a different viewpoint.
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