renormalization - Why does the counterterm's propagator have inverse units of the propagator? $phi^4$-theory

Saturday, October 12, 2019

According to Peskin & Schroeder (page 325), the Feynman rule for the counterterm

 ------(x)-----

for

$$ \frac12 \delta_Z(\partial_\mu\phi_r)^2-\frac12\delta_m \phi_r^2$$

being $\phi_r$ the renormalized field, is given by

$$i(p^2\delta_Z-\delta_m)$$

which resembles rather the (multiplicative) inverse of the propagator for the original Lagrangian (whith physical quantities). Why?

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