- #1
hyungrokkim
- 3
- 0
In Michio Kaku's QFT book, p. 106, he writes:
[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]?
[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]?