in QFT Lagrangian what is the potential energy exactly?

alemsalem

if I have χψ*ψ term in the Lagrangian, the scattering ψψ→ψψ behaves as if we had a potential (non-rel. limit) Exp(-mr)/r.
but when I try to calculate the expectation value of χψ*ψ in any state I get zero.
is that a different kind of potential energy? does it have to do with re-normalization?

Thank!!