Attractive Feynman diagrams and virtual photons

Question

In the electromagnetic interaction a photon is exchanged which can cause a repulsive force between to charged particles like the electron/electron or up/up quarks interactions. But when i look at the Feynman diagram two opposite sign charges the attractive force is also mediated by the photon. This is strange as a transfer of momentum by an intermediate particle would not cause two objects of unlike charge to come together but repel. I read in another post on this forum that it should be interpreted like a boomerang effect. But the photon does not do this. It goes from one particle directly to the other one. Can someone explain what is happening really? That is quantum mechanically?

Answer 1

This is a good question and if you look at the virtual particles classically, then such a thing is indeed impossible. But you should not look at Feynman diagrams as "real processes" but mathematical tools in particle interaction calculations. When you do such calculations, the charge sign in the calculation appears at the vertices and the propagator (photon) does not carry information on the specific values of the charge directly.

For a quantum mechanical explanation, we can do this (roughly) by consider Heisenberg's uncertainty principle i.e.,

$$\Delta x \Delta p \ge \frac{\hbar}{2}$$

Recall that if we are calculating momentum transfer between two particles which are (almost) localised then they have a well defined position meaning that the momenta will be extremely uncertain. A virtual particle with a specific momentum will therefore correspond to a wave with a wavefront spread all over space due to uncertainty in position. Because this wavefront is spread everywhere, either particle can create the photon anywhere and the other can absorb it anywhere meaning either can get a "kick pushing it" in the direction of the other particle which would correspond to an "attractive force".

Once again it should be stressed that you should never view virtual particles in Feynman diagrams as having the trajectories of particles in classical physics.