I have two questions about photon momentum in QED, which I think are related.

1. In Peskin and Schroeder, p. 186, they deduce that the vertex correction must be of the form

$$\Gamma^\mu = \gamma^\mu\cdot A + (p'{}^{\mu}+p^\mu)\cdot B + (p'{}^{\mu}+p^\mu)\cdot C,$$

where $p^\mu$ is the momentum of the incoming electron and $p'{}^\mu$ is the momentum of the outgoing electron. Now, my question is why the second term vanishes when dotted with $q_\mu$, the momentum of the scattering photon, as does the first when sandwiched between $\overline{u}(p')$ and $u(p)$?

2. On page 191, they say that $q^2 < 0$ for a scattering process. But if $q$ is the momentum of a photon, shouldn't its square always be zero?

I have two questions about photon momentum in QED, which I think are related.

1. In Peskin and Schroeder, p. 186, they deduce that the vertex correction must be of the form

$$\Gamma^\mu = \gamma^\mu\cdot A + (p'{}^{\mu}+p^\mu)\cdot B + (p'{}^{\mu}-p^\mu)\cdot C,\tag{6.31}$$

where $p^\mu$ is the momentum of the incoming electron and $p'{}^\mu$ is the momentum of the outgoing electron. Now, my question is why the second term vanishes when dotted with $q_\mu$, the momentum of the scattering photon, as does the first when sandwiched between $\overline{u}(p')$ and $u(p)$?

2. On page 191 below eq. (6.44), they say that $q^2 < 0$ for a scattering process. But if $q$ is the momentum of a photon, shouldn't its square always be zero?