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I’m reading Peskin & Schroeder as a first intro in QFT. The first half of chapter 4 is spent on calculating the 2-point correlation function in $\phi^4$ theory:

$$\langle \Omega | \phi(x) \phi(y) | \Omega \rangle$$

So far, P&S have shown that to first order the only contribution is

$$ \propto \int d^4 z D(x-z) D(y-z) D(z-z)$$

My question is: isn’t the term $D(z-z)$ divergent? Is this where renormalisation comes in?

When googling I saw some references to renormalisation in $\phi^4$ theory but I still want to ask, because P&S wait another five whole chapters before introducing renormalisation. It feels bad practice to expose the student to it so early and then pretend nothing is going wrong =p

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    $\begingroup$ Unfortunately, a large number of QFT textbooks/courses insist on bum-rushing to quantum electrodynamics before giving you a good intuition for what a QFT is fundamentally. This leaves students wrestling with gamma matrices and polarization sums without them having tackled a lot of basic issues present in any QFT. $\endgroup$ Apr 30, 2021 at 19:00

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Yes it is. It is the one-loop correction to the two-point function and needs to be regularised. This is explained in detail in P&S.

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