〈 Berger | Dillon 〉

dim reg is a subset .. he shows regulator independence

so the method of regulation is irrelevant because they’re all the same asymptotic expansion

I think my point is that it’s weird to even call dim reg a “regulator” because the way it’s implemented is completely unrelated to the “add a smooth regulator to a sum/integral) method this type of math uses. Something about analytically continuing in the dimensionality of your..

spacetime is fundamentally more sketchy than, say, energy cutoff regularization. And the fact that dim reg works seems completely unrelated to the regulator independence for formally divergent integrals/sums.

I see what you’re saying .. that’s how it seems at first .. but that’s just cause it’s formalism is annoyingly sophisticated

Here’s another way to see why it’s sketchy: what dim reg basically does it takes a function that is defined on the natural numbers and “analytically continues” it to a function defined on the whole complex plane. However, analytic continuation is only unique for functions...

...defined on an open neighborhood of the complex plane. The function (value of the integrals) on the natural numbers has, hypothetically, many different analytic continuations. The fact that we have a convenient one in terms of gamma functions is just one choice of many.

look .. I agree with everything you’re saying .. but imo renormalization is a symptom not the illness .. there’s so many bigger things to worry about with QFT when literally the fucking interaction picture doesn’t even exist