- #1

olgerm

Gold Member

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## Main Question or Discussion Point

I have some questions about this video. I have watched other videos in this series. Otherwise very nice series, but I think there may be mistake. Isn't the video flawed because it forgot forgot 0'th component of 4-fector ##A## aka ##\varphi## in 3-vector representation, I think it because lorentz gauge conditiond should be ##\partial_t A_t +\partial_x A_x +\partial_y A_y +\partial_z A_z=0## not ##\partial_x A_x +\partial_y A_y +\partial_z A_z=0## like video in 8.05. Also one maxwell equations ##\partial_t^2 A_0=\nabla^2 A_0## aka ##\partial_t^2 \varphi=\nabla^2 \varphi## is missing.

what is the 4-potential field ##A## if i have occupation number 1 for ##n_{1,0,0;2}## (##k=[1,0,0]## and ##\alpha=2##) and other occupation numbers are 0?

How are these photon occupation numbers related to 4-potential field ##A##. Most confusing is that for each wavenumber k they have only 2 integers although for any wave there are more degrees of freedom(2 numbers more). Or quantum description of EM-field has less degrees of freedom?

what is the 4-potential field ##A## if i have occupation number 1 for ##n_{1,0,0;2}## (##k=[1,0,0]## and ##\alpha=2##) and other occupation numbers are 0?

How are these photon occupation numbers related to 4-potential field ##A##. Most confusing is that for each wavenumber k they have only 2 integers although for any wave there are more degrees of freedom(2 numbers more). Or quantum description of EM-field has less degrees of freedom?