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369. assignment (photon)

It is usually said that photons are the force carriers or the mediators of the electromagnetic forces between electric charges. At the same time we know also that electromagnetic waves on the quantum level are described in terms of photons.

It seems to me that we have 2 types of photons:

 

    the photons which mediate the electromagnetic interactions which are offshell hence their masses do not necessarily have to be zero, I suppose
   

and the photons which are the quanta of electromagnetic waves which are massless.

 

Am I correct, or am I confused and missing something?

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