Abstract
We present an analysis of the dispersion relations in the light cone time- (\ensuremath{\tau}-) ordered perturbation theory with a rotation average procedure. For an explicit example of the analysis, we present the calculation of the two-body scattering amplitude that corresponds to the box Feynman diagram in the ${\ensuremath{\varphi}}^{3}$ theory. Using a rotation average procedure, not only the contribution of an individual time-ordered diagram can be quantified in a Lorentz invariant way but also the number of \ensuremath{\tau}-ordered diagrams that yield the imaginary parts can be reduced by half even if the masses of the two bodies are not the same. As shown in this example, the total amplitude can be obtained by calculating only the imaginary parts of the \ensuremath{\tau}-ordered diagrams without explicitly invoking the higher Fock-state contributions. Our numerical results confirm that the dispersion relation is satisfied not at the level of individual \ensuremath{\tau}-ordered diagram but at the level of the total Feynman amplitude.
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