Chris Oakley wrote:
[quoting Dan Solomon:]
>>So this is the way I look at the QFT "recipe". It works but it doen't
>>look like a fundamental theory. There must be something else behind
> This is very well put, and begs the question, "Why is turning the recipe
> into a theory generally considered such a low-priority task?"
Because people usually put their priority on what they find tractable.
Surely there is something fully rigorous behind it, but the
nonperturbative theory is very difficult functional analysis
which no one knows how to attack.
The perturbative theory (clearly not fundamental since it stops
short of producing actual functions) is already completely
understood through renormalization group arguments, though you
don't seem to like it. But it is unlikely to get any neater
by further tinkering with it, so nobody is interested in wasting
their time. Those who look for a challenge rather try to get
directly at the nonperturbative case.