Re: Lambda QCD

Darth Sidious wrote:

> > In my opinion, continuation alpha to (0..Lamda) region has no phisical
> > sence, only formaly value.
>
> Why not? The thing is that we can calculate the beta function with some
> confidence only in the small coupling (high energy) regime.

Main reason - we can't establish connection between alpha and
_observables_.

> If the coupling constant
> does not go to infinity, the continuation to energies below Lambda does
> not encounter any obstruction.

At energies below Lambda come to play effects of nontrivial physical
vacuum. For example non zero effective gluon mass. So no sense to
introduce alpha. Of course, we can formally evaluate alpha, but what for
?

> I stongly disagree. As far as I know, the QCD path integral gives a
> *complete* non-perturbative definition of the theory, the strong
> coupling regime included.

Yes, but this is only formally construction like string theory. Why are
you think that it describe _reality_? May be, but lack of confidence.

> Yes, this is the dimesional transmutation. However, this Lambda is not
> like the other dimensionful parameters in renormalisable theories. In
> these theories the dimensionful parameters are there in the begining as
> bare parameters, whereas Lambda_QCD arises when taking off the cut-off.

There are big difference. In theories like QED, existence Lambda signal
about incomplete of theory in ultraviolet. In QCD - incomplete in
INFRARED. In ultraviolet case no reason to worry because no ultraviolet
degree of freedom in lab. In infrared case - all significant for us
events are infrared. So QCD is incomplete to describe our infrared
world.

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