In Michio Kaku's QFT book, p. 106, he writes:(adsbygoogle = window.adsbygoogle || []).push({});

[To illustrate problems with direct quantization due to gauge invariance]

let us write down the action [of the Maxwell theory] in the following form:

[tex]\mathcal L=\frac12 A^\mu P_{\mu\nu}\partial^2A^\nu[/tex]

where

[tex]P_{\mu\nu}=g_{\mu\nu}-\partial_\mu\partial_\nu/(\partial)^2[/tex]

The problem with this operator is that it is not invertible. [...]

I don't understand his notation. Normally, the same Lagrangian is written

[tex]\mathcal L=-\frac14F^2[/tex]

When factoring out [tex]A^\mu[/tex], how does he get the [tex]\partial^2[/tex]?

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# Maxwell propagator in Kaku's QFT book

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