In Peskin's QFT book page 294, he formally addressed the quantization of EM field,

$$propagotor_{EM}=\frac{-ig_{\mu\nu}}{k^2+i\epsilon}$$ Now that we have the functional integral quantization method at our command, let us apply it to the derivation of this expression.
Consider the functional integral
$$\int DAe^{iS[A]},$$

Actually I expected to see how he would derive the generating functional $\int DAe^{i(S[A]+J^\mu A_\mu)}$ from the canonical quantization before proceeding on to introduce the Faddeev-Popov trick.

So is there a way to do this derivation, i.e., from the operator formalism using Hamiltonian, or we must presume the validity of this path integral as a starting point, which is probably what Peskin did(I guess)?


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