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When I was reading the lecture notes Advanced Quantum Field Theory by Jorge Crispim Romao, I accidentally found the following thing that I don't understand.

On page 56, section 2.2, the author defined the creation operator that creates an in state of a scattering process. The bare Lagrangian is given by

$$\mathcal{L}=\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{4!}\phi^{4}.$$

The operator $\phi_{in}(x)$ creates the in state. This operator is a functional of $\phi(x)$. As far as I understood from my previous education, the in/out state has physical mass, and that is why we do not consider diagrams that have loop corrections to external legs. That is to say, the mass of the in state should be the renormalized physical mass, not the bare mass.

However, equation (2.10)

$$(\Box+m^{2})\phi_{in}(x)=0$$

shows that the mass of the in state is the bare mass.

Did the author make a mistake here?

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