Say one has the following Lagrangian: $$ \mathcal{L}=\frac{1}{2}(\partial_\mu\phi_r)^2-\frac{1}{2}M^2\phi_r^2+g\phi_r^3+\frac{1}{2}(Z^2-1)(\partial_\mu\phi_r)^2-\frac{1}{2}(Z^2-1)M^2\phi_r^2-\frac{1}{2}Z^2\delta M^2\phi_r^2+\delta gZ^3\phi_r^3+(Z^3-1)g\phi_r^3. $$ How would like to identify the free part $\mathcal{L}_0$ and the interaction part $\mathcal{L}_\text{int}$ in order to calculate the free theory propagator and other stuff. However, I am not sure whether one should only put the first two terms in $\mathcal{L}_0$ or $\frac{1}{2}Z^2(\partial_\mu\phi_r)^2-\frac{1}{2}Z^2M^2\phi_r^2$.


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