Re: Renormalization
- From: Aaron Bergman <abergman@xxxxxxxxxxxxxxxxxx>
- Date: Sun, 24 Apr 2005 01:17:29 +0000 (UTC)
In article <1114268033.464640.137600@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
jsolomon@xxxxxxxx wrote:
> What you, and others, are saying is that, we should at this
> point, redefine the integral by the process of dimensional
> regularization. I think that you are saying that we must incorporate
> the process of dimensional regularization as a postulate of the theory.
> Is this correct?
I haven't been paying too much attention to this discussion, but no.
Dimensional regularization is just some type of regularization -- there
are others. The problem is that, you've stuck the wrong thing in the
path integral. Lagrangians with finite couplings only make sense in
cutoff theories, unless they're conformal. Thus, the only theories that
make sense are fixed points and some infinitesimal perturbations
thereof. Unless you have something nice in the UV, you end up with
short distance singularities which are what you encounter in these
integrals [1]. If you're ignorant about the UV or just don't want to
worry about it, you can cutoff these integrals in various ways to get a
finite answer. The procedure of renormalization is how you take these
cutoff results and get something that makes sense and is independent of
the UV completion of the theory. Dimensional regularization is a
particularly nice way of regularizing in that it preserves gauge
invariance, but, as I said, there are others.
Aaron
[1] You can also have IR divergences, but those usually mean something
else like that you're expanding around the wrong background.
.
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- Re: Renormalization
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