Re: Clarify of Yang Mills and Mass Gap Hypothesis Problem

Chris Oakley wrote:

> "Arnold Neumaier" <[EMAIL PROTECTED]> wrote in message
> news:[EMAIL PROTECTED]

> > ieee std wrote:

> > Not even QED is a mathematical object, although it is the theory
> > that was able to reproduce experiments (Lamb shift) with an
> > accuracy of 1 in 10^12, and with less accuracy already in 1948.
> > But till today no one knows how to formulate the
> > theory in such a way that the relevant objects whose
> > approximations are calculated and compared with experiment
> > are logically well-defined.
> 
> I do not believe that this is correct. 

You may wish to look at the discussion in sci.physics.research at

http://groups.google.com/groups?q=g:thl2927696240d&dq=&hl=en&lr=&ie=UTF-8&selm=1b7c3dda.0303101446.45929b31%40posting.google.com

> It is possible to have a rigorous QED, it is just that it is not
> clear (to me, at least, at this time) how one calculates the higher
> order effects (i.e. the Lamb shift in the one-electron atom & the
> anomalous magnetic moment of leptons).

But these are precisely the effects for which QED is famous.
 
> See
> 
> http://www.cgoakley.demon.co.uk/qft/qedwip.pdf

At the end of 

http://www.cgoakley.demon.co.uk/qft/corres.pdf

which shows how many problems your work has, you give witness to 
the fact that your paper didn't generate any feedback and was 
never cited. If your paper were the answer to old unsolved 
questions, the response would have been quite different.

> Free field theory is rigorous & if one writes the interacting
> fermion/photon fields as sums of tensor products of free fields
> (Haag expansions) then one can obtain matrix elements by inspection
> knowing the free field (anti-)commutators.

No, one only gets coefficients of an asymptotic expansion of matrix
elements, which is likely to be divergent, and no one knows how to
make rigorous sense of it. So what is rigorously defined are just
approximations to something that should exist in a rigorous theory,
and it happens that in QED these approximations are highly accurate.

The state is comparable to the knowledge about pi at the time
of Archimedes. He had good accuracy and a scheme to improve it,
bu there was no theory in which real numbers like pi were well-defined.

Your work does not go beyond this, since it only produces
a power series expansion without a convergence proof, and is
not even able to produce the Lamb shift.

> I might supplement Dr. Neumaier's comments with the observation that
> the fabled accuracy of renormalised QED is nothing of the sort. All
> the "theory" proves is that you can get any answer you like by
> subtracting infinity from infinity.

No, one does not get anything one likes but a well-defined
answer which agrees with experiment, and one does not need to 
subtract any infinities if the right approach is used. 
See the book on QED by Scharf.


Arnold Neumaier