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TriTertButoxy
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If you inspect the QED lagrangian, you'll find that the electromagnetic vector potential must have the units of [1] energy.
According to Peskin and Schroder's QFT text, the expansion of the electromagnetic field operator is
3 factors of energy from [itex]d^3p[/itex], and -1/2 factor from [itex]1/\sqrt{2E_{\mathbf{p}}}[/itex]. If the polarization vectors, [itex]\epsilon_\mu^r[/itex], are unitless, then the ladder operators must carry units of 1½.
How are the photon states normalized?
According to Peskin and Schroder's QFT text, the expansion of the electromagnetic field operator is
[tex]A_\mu(x)=\int\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_{\mathbf{p}}}}\sum_{r=0}^3\bigg(a_{\mathbf{p}}^r\epsilon_\mu^r(p)e^{-ip\cdot x}+a_{\mathbf{p}}^{r\dagger}\epsilon_\mu^{r*}(p)e^{ip\cdot x}\bigg).[/tex]
3 factors of energy from [itex]d^3p[/itex], and -1/2 factor from [itex]1/\sqrt{2E_{\mathbf{p}}}[/itex]. If the polarization vectors, [itex]\epsilon_\mu^r[/itex], are unitless, then the ladder operators must carry units of 1½.
How are the photon states normalized?
[tex]\langle0|a_{\mathbf{p}}^ra_{\mathbf{p}}^{r\dagger}|0\rangle=?[/tex]