I assume that if your theory has an interaction term written as L(adsbygoogle = window.adsbygoogle || []).push({}); _{I}= ±λ*fields, where λ is the coupling, that the 1PI vertex is defined as:

$$i(\pm \Gamma)=i(\pm \lambda)+loops$$

That way to tree level, Γ is λ, and not -λ. The exception seems to be the self-energy. A mass term has -m^{2}*field^{2}, so this suggests that you should write -i Π whenever you insert a self energy. However, it seems textbooks write +iΠ for self-energy insertions. This leads to propagators that look like:

$$\frac{i}{p^2-m^2+\Pi(p^2)}$$

where Π has the opposite sign of m^{2}.

Is it conventional to define the self-energy with +i instead of -i, so that in the propagator it has the opposite sign of the mass? Why is this so?

Also, is the self-energy even a 1PI vertex? Don't you have to include the tree-level term? So really:

$$i\Gamma^{(2)}=-i(p^2-m^2+\Pi(p^2) )$$

Or should it be defined:

$$-i\Gamma^{(2)}=-i(p^2-m^2+\Pi(p^2) )$$

It's not clear how to logically define the sign of Γ^{(2)}. Should it be the same sign as m^{2}, or Π(p^{2})?

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# 1PI vertex conventions

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