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This is an excellent question. The technical term for this effect is a collinear divergence. When $p_i-p_f$ tends to $0$ you get a divergence in the scattering amplitude. So why is this physically reasonable? Well remember that actual physical observables are cross-sections, not scattering amplitudes. Also recall that you cannot prepare a particle with an ...


Now per QED, electrical charges interactions are effected by photons. Suppose you are one of the two charges. How do you know to attract or repel the other charge? You want something that does not exist - intuitive picture of physical process within a theory which is a demonstration of how far can one go with mathematisation of experience and ignoring ...


The frequencies are the same but they are 180 degrees out of phase with each other.


I only expand TwoBs comment to your answer. There is following statement: massless particles with both of helicities $\pm 1$ can't be represented by 4-vector field $A_{\mu}$. The only field (up to equivalence) which represents corresponding particles is $F_{\mu \nu}$. If you decide to represent these particles by $A_{\mu}$, then it won't be 4-vector: $$ ...

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