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We present on shell-scheme for the 2PI formalism with a particular focus onthe renormalized equations of motion. We first revisit the so-called Hartreeapproximation where we give the counterterms for both the broken and unbrokenphase. Moreover, we give explicit formulas for the renormalized three- andfour-point functions in the broken phase. We then turn to the sunsetapproximation, with only scalars and then including fermions. We give explicitformulas for the wavefunction and mass counterterms. Moreover, we show that, inparticular, the two-point functions can be obtained numerically in a fastconverging scheme even for large couplings of order one.

Renormalized equations of motions for scalars and fermions in the 2PI formalism