〈 Berger | Dillon 〉

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

We’re playing with fire this whole time and it’s got to burn us at some point .. it just seemed that we’ve pushed the fire Into the very last step of computing observables

And this is why it absolutely confounds me that, regardless of all of the problems with QFT.. That. Shit. Works.