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The photon will have a vector of P=(E,p), where p^2=E^2, so P^2=0, since photons don't have mass.

It must be that P = P1 + P2, where P1 and P2 are electron and positron.

P1 = (E1,p1), where E1^2 = p1^2 + m^2.

So (E,p) = (E1,p1) + (E2, p2) = (E1+E2,p1+p2)

So (E,p)^2 = 0 = m^2 + m^2 + E1*E2 - p1*p2

So is the product of p1 and p2 really equal to m^2 + m^2 + E1*E2?!

That would suggest that either p1 or p2 is greater than it's corresponding energy, which would make mass negative.

What am I missing?