Reminds me now of the wonder I felt as after a few classes that had us doing integrals of various tedious geometries for EM fields, we come to QM - the really h

Reminds me now of the wonder I felt as after a few classes that had us doing integrals of various tedious geometries for EM fields, we come to QM - the really hard course - and we just pop a Dirac delta in to trivialize some integrals. It's like suddenly being able to say, "Enough! Just tell me the value right there!" Which turns out to reduce to your friendly neighborhood point particle model. (Pretty much by design, if I'm not forgetting my history correctly - it's sort of a made up tool that sort of abuses notation, like the Heaviside step function.) But deep down I never trusted that a particle was actually a basically zero dimensional-like point, though. It was just useful to think of it as one.