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Feynman diagrams are a pictorial way to keep track of terms in quantum field theory calculations. Each element of a Feynman diagram represents a different term in our calculation.
An example can be seen on the right-hand side.
Feynman Rules Resources:
It struck Feynman that everyone had a favorite principle or theorem and he was violating them all… Feynman knew he had failed. At the time, he was in anguish. Later he said simply: “I had too much stuff. My machines came from too far away.”[…] Schwinger’s students at Harvard were put at a competitive disadvantage, or so it seemed to their fellows elsewhere, who suspected them of surreptitiously using the diagrams anyway. This was sometimes true… Murray Gell-Mann later spent a semester staying in Schwinger’s house and loved to say afterward that he had searched everywhere for the Feynman diagrams. He had not found any, but one room had been locked…from "Genius" by Gleick