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How were particle physics calculations done before feynmanFeynman diagrams?

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How were particle physics calculations done before feynman diagrams?

I've seen and read that calculations before Feynman diagrams involved solving differential equations, but I can't find sample calculations like these. I've read that they would take months and pages to do, so I'm curious what the equations were that were being solved. Does anyone know an old textbook or papers where these are shown?