Can anyone provide an elementary argument for why the zero mass of the photon means that it can't be longitudinally polarized?(adsbygoogle = window.adsbygoogle || []).push({});

I know of at least one non-elementary argument, which is that if you write down the Proca equation, it only has longitudinally polarized solutions if the mass is nonzero. This is fine, but seems to me to be very indirect.

I know of a couple of elementary arguments that prove the converse: that you can't put constraints on the polarization or helicity of a particle unless it has zero mass. (E.g., +1 helicity could be -1 helicity in a frame where you were catching up with the particle. Or you could go into the particle's rest frame, in which case there's no preferred direction, so it has to have all three axes of polarization available.)

What I'm looking for is an argument that proves the original statement, not its converse, and that's more elementary than solving the Proca equation.

It would be interesting to know whether there's a similar reason that the graviton can't have zero helicity.

Thanks in advance!

-Ben

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# Elementary argument against longitudinal photons?

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