My question is related to the interpretation of antiparticles. According to the so called Feynman-Stueckelberg interpretation a negative energy solution of the Dirac equation corresponds to a positron which then runs apparently backwards in time. But if I consider the vertex of a electron-positron annihilation I have at this vertex an incoming electron with positive energy which under "emission" of a virtual photon turns into a (the vertex) leaving positron which runs backwards in time. But this way several conservation laws seem to be violated.
I would in fact expect the positron not to leave the vertex but entering the vertex. In that case the conservation laws would be fulfilled.
However, for me a solution of ~exp(iEt) is either a negative energy electron running forwards in time or a positive energy positron running backwards in time. But I cannot fit that with the electron-positron annihilation (see above). I would be grateful if somebody could dissipate by confusion.