For example, let's consider the electromagnetic interaction between a massless fermion and a electromagnetic externel sourse $A^\mu$, then the lagrangian is
$$\mathcal{L}=\bar{\psi}\gamma^\mu\partial_\mu\psi+ieA_\mu\bar{\psi}\gamma^\mu\psi$$
and how can we calculate the Feynman diagram and $\mathcal{M}$ of it?

But according to relativity, the equation of motion of a particle with charge is
$$e F^a\ _bU^b=U^b\partial_bP^a$$
where $F_{ab}$ is the electromagnetic tensor, $U^a$ is the 4-velocity of the particle and $P^a$ is the 4-momentum of the particle. If the particle is massless, then the speed will be $1$ and this equation fails.

So can a massless particle have charge and interaction with externel sourse? If could, for example, how can I calculate the force and equation of motion? If couldn't, why?

This post imported from StackExchange Physics at 2014-04-13 12:29 (UCT), posted by SE-user user34669