Dimensional regularization is just high-level bullshit
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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
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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...
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...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.
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