Feynman diagrams show a very definite process with these particles coming in, this interaction occurring, and those particles going out. Given that all of this describes waves in a field would there be other, unimportant virtual particles created that are not shown in the diagram that just dissipate away - essentially hairs in the diagrams? Would it even be possible to predict these hairs?
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The probability amplitude for a process is computed$^\dagger$ by summing all possible Feynman diagrams, given the initial and final states. So a Feynman diagram does not describe a single, specific way that the process occurred. I think of it as one possible way the process could happen, and due to quantum weirdness all possible ways the process could happen contribute to the final answer.
$^\dagger$ At least, perturbatively, although there can also be non-perturbative effects not captured by Feynman diagrams.
Andrew
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A Feynman diagram represents one particular possible path between incoming and outgoing particles. But in general there will be many (often an infinite number) of possible paths between the same inputs and outputs. The trick is to find a way to add up the contribution from each of these paths to get a probability amplitude for the overall interaction. Usually the sum cannot be calculated exactly and must be approximated.
gandalf61
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