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Electron Positron pairs can be created via three process:

  1. Photon-Photon interaction
  2. Photon-Particle interaction
  3. Particle-Particle interaction

I want to know how 2. and 3. can create electron - positron pair.

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    $\begingroup$ Is the answer "as long as they have enough excess energy" not enough for you? What kind of answer are you looking for? $\endgroup$
    – Floris
    Commented Jun 23, 2015 at 5:38

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Electron positron pairs can appear whenever there exists enough energy and electromagnetic interactions.

Photon photon to produce an e+e- is disfavored as far as crossections go because of the great number of vertices involved in the Feynman diagram

two photon

One of the outgoing photons, if it has enough energy can be a virtual photon in a diagram creating a pair , joining a) with the two photon diagram.

photon to e+e-

The same is true for photon-particle and particle-particle particle interactions, a virtual photon with enough energy creates an e+e- pair.

genericdiagram

The outgoing photon can be virtual and given enough energy can produce e+e- pairs .

To learn about putting together Feynman diagrams have a look here.

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