Good, the photon is still elementary and not a composite. Is that kind of like how a vector can be considered mathematically to be the sum of 2 virtual orthogonal vectors forming a right triangle where the hypotenuse is the photon?
Not a sum but a rotation. You have a basis made of B and W3, you rotate the axis by a rotation of the electroweak mixing angle, and you end up with another basis made of the photon and the Z-boson. You can check my answer to @muphy's comment above. This can help too.
All photons are the same, except for their frequency.
The photons are the same guys. Different frequencies means different energies, but these are still the same photons :)
It is still not clear to me how the information of the charge of the electron or positron is transmitted between particles via photons, except by the sign of the electric fields generated by the particles.
It is not transmitted. Please see below where I try to explain :D
Your diagram shows repulsion. Are you saying that attraction requires pair annihilation and then pair production?
In quantum field theory, you need to get all possible diagrams for a process to compute what is going on. We have three considered processes here:
- electron + electron => electron + electron
- electron + positron => electron + positron
- positron + positron => positron + positron
In the case of electron-positron scattering, you have one more diagram which changes everything.
I actually plan to discuss this more in details in the course #4 (for which I will draw extras stuff). I hope the information I provide here is enough. Otherwise, please shoot again on me :p