It's the current state of the art anyway. But also it's worth mentioning it's more complex than just a function x^2. When looking at a Feynman Path Integral you integrate an Operator (mapping a function to a function) over a an uncountable domain of functions. The other approach which is used to calculate probabilities goes with an approximation that cannot be used for simulations though. All this is not mathematically bullet-proof as Mechanics also speaking about Wightman axioms. (And even in Mechanics it's possible to construct infinities)