In QED, photon number is not conserved and photons can produce electron-positron pairs in the vacuum.
But if we take away electromagnetism and have a pure electron theory. Does this still produce electron-positron pairs in the vacuum?
i.e. starting with a single electron, in the free theory is there zero chance of detecting two electrons and a positron at a later time? There is no Feynman diagram that can do this....
On the other hand I hear a lot about electron-poistron pairs being created out of the vacuum. I can understand this would happen near a black hole if a high energy graviton decayed into an electron-posistron pair.
In the free theory even if electron-posistron pairs were created and destroyed would they have any impact if they can't interact with ordinary electrons via electromagnetism?