Re: Connes & Marcolli paper on renormalization

From: Matthew Nobes (drnobes_at_gmail.com)
Date: 10/11/04 

Date: Mon, 11 Oct 2004 08:52:19 +0000 (UTC)

"Chris Oakley" <coakley@cgoakley.demon.co.uk> wrote in message news:<ck2v5d$mg2$1$8300dec7@news.demon.co.uk>...
> > Well, you can throw out the theory, but that seems a bit drastic.
>
> I believe that one has no choice.

Of course one has a choice. You regulate the theory, and investigate
the consquences of doing that.

> One can in any case find holes in the
> cutoff procedure. Supposing, for example, we were to choose Lambda as a
> function rather than a constant. Furthermore, let us make it a function of
> variables that never even entered the original equations. There is no reason
> in principle why we should not be allowed to do this. We then very rapidly
> get nonsense. You will then say that it was my own fault for not making it a
> constant, but all that means is that you can find a path through the
> minefield. It does not mean that the minefield has ceased to exist.

The cutoff in *by*definition* an energy much much greater than the
energies you're interested in. It can be a function of any variables
you like, but it must always be much greater than the scale you're
interested in. I have no idea what you think this example proves.

[snip]
> You and Dr. Neumaier say that it is
> "unreasonable" to have four-momentum integrals extending to infinity,

Yes, it's unreasonable to expect that QED is the be all and end all of
physical theories. I have no idea why you find that a controversial
point.

> I say that if the mathematical logic
> leads one there, then one has no choice other that to accept it, and if this
> leads to nonsense then one has to accept that that something is
> fundamentally wrong with the approach.

What "logic" leads you to integrate to infinite momentum? Physics is
not pure mathematics, you're allowed to make arguements like "this
theory is not expected to work at 10 TeV, therefore I won't integrate
out past that".

                                                         Matt

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