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There are infinitely many. But the cool math that Feynman worked out is that infinite diagrams (paths) kinda look random, unless they’re not random (aligned).
When you get enough infinite “randombess” you tend to cancel almost everything out (not actually random but phases that destructively interfere), so what you’re left with (when you “sum all paths”) are solutions that favour a particular direction or phase.
I absolutely love the concept of chaotic systems that mathematically stabilize towards order.