Ciro Santilli
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I think they are a tool to calculate the probability of different types of particle decays and particle collision outcomes. TODO Minimal example of that.
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And they can be derived from a more complete quantum electrodynamics formulation via perturbation theory.
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At Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), an intuitive explanation of them in termes of sum of products of propagators is given.
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Ancestors

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