Question

Does the free electron theory have electron-positron pair creation?

Answer 1

During β+ decay, a proton is converted into a neutron and a positive beta particle or β+. This is called a positronand has the same mass as an but the opposite charge (positive). When anelectron and a positron collide an annihilation event occurs and gamma rays are produced.

Answer 2

In free theories there is no creation nor annihilation of anything, precisely because they are free. I don't understand the question. In pure electron theories, the leading interactions are given by non-renormalisable terms a la Fermi.