It is very interesting that the most accurate theory in existence, based on comparison to experimental results, is quantum electrodynamics or QED. Yet its derivation is not at all rigorous. It involved the 'trick' of renormalization. In the renormalization of QED, what you do- that is, what Feymann first did- is to replace the infinity that QED calculates for the electron mass and charge, by their real or actual measured values.

There is no known reason why this should work. I would guess that it was an act of desperation on the part of Feymann. The more rigorous physicists like Schwinger, working on the same theory, probably would never think of doing such an ad hoc thing. Yet it produced the most accurate theory ever. And it invented the idea of renormalization for physics, which was then used for QCD, the electroweak theory and the Grand Unified theory. Renormalization does not work for gravity, hence the invention of string theory that predicts finite results for everything without renormalization. But string theory requires supersymmetry which is yet to be found experimentally.

Wanda