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]?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Maxwell propagator in Kaku's QFT book

**Physics Forums | Science Articles, Homework Help, Discussion**