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I recently read that a virtual photon has mass, unlike a real photon.

"As a consequence, a real photon is massless and thus has only two polarization states, whereas a virtual one, being effectively massive, has three polarization states." https://en.wikipedia.org/wiki/Virtual_particle

"In that theory, the mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as renormalization." https://en.wikipedia.org/wiki/Photon

So here is my question: how does a virtual photon get its mass?

Does it acquire its mass through interaction with the Higgs Field, like $W$ and $Z$ bosons, or is its mass generated in another way?

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    $\begingroup$ The virtual photon does not "get mass" because it is not associated to any actual particle state. For more on misinterpretations of virtual particles, see e.g. my answers at physics.stackexchange.com/a/201741/50583 or physics.stackexchange.com/a/275099/50583 $\endgroup$ Commented Oct 31 at 18:02
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    $\begingroup$ On top of the definitely relevant answers by ACM above, I have been routinely pointing out that this is really an artefact of the perturbation method that is covariant. Back in basic QM, the perturbation method that is taught, makes it such that the intermediate calculations involve a lot of situations where the energy is not fixed onto the correct value that it should be. That corresponds to the QFT version of OFPT where everything has the correct masses, but the energy is again seemingly allowed to be wrong. $\endgroup$ Commented Oct 31 at 19:27
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    $\begingroup$ The Old Fashioned Perturbation Theory (OFPT) is manifestly breaking Lorentz invariance by treating energy and momentum very differently, and so it makes a lot of the calculation details very difficult to work with. Changing the perturbation method to a covariant one, would then require us to find another thing that is related to both energy and momentum, that is manifestly Lorentz invariant, in order to sweep the wrongness into, and that thing is obviously the mass. That is how virtual particles have wrong masses. However, take ACM's advice to heart: this is not saying something about reality. $\endgroup$ Commented Oct 31 at 19:30

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