The electromagnetic interaction, with the photon as mediator, has been the model for the others. That is because Quantum Electro Dynamics (QED) has shown an impressive agreement with experimental results (theory and experiment agree with a certainty of one in a million!), but also because QED may be formulated in a very powerful way as a, so called, gauge theory. This means it uses quantum mechanical symmetries to explain how the interaction works. The basic Feynman diagram of electromagnetism looks like:
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