# Talk:Yang-Mills equations

### From DispersiveWiki

This page was derived from an earlier version which had corrections and suggestions from Jacob Sterbenz.

I've removed the arguments based in FraE2007 as they appear to be incorrect. (The "mapping theorem" in Theorem 1 of that paper does not appear to have a valid proof; an extremum for the Yang-Mills functional for a restricted class of fields is not necessarily an extremum for the Yang-Mills functional for the entire class of fields.) Similar adjustments will be made elsewhere in the Wiki. Terry 20:12, 28 February 2009 (UTC)

It is my personal conviction that you misunderstood the content of the theorem. It is just claimed that exists a class of solutions common to both functionals. A solution of the equations is always an extremum but, of course, this cannot be overall true. In order to prove that this is wrong you should prove that classical solutions are not common to the scalar field and Yang-Mills field as you claimed in your comment on Wikipedia. --Jonlester 19:32, 10 March 2009 (UTC)

- It may be possible to have some common solutions to both theories but the point is that the proof in FraE2007 is seriously incomplete. Tumur 21:07, 10 March 2009 (UTC)

Tumur, it is the same old problem. I am a physicist (even if I have written math papers also, e.g. [1]). The question is quite simple. Why to rely on a generic mathematical evidence that may fail here when by a simple substitution of my solution into Y-M eqs. I am easily proved right?--Jonlester 09:47, 11 March 2009 (UTC)

Please, check my blog here. Terry's criticism does not apply to my case. These solutions exist and the text should be re-entered into this entry of DW. Thank you.--Jonlester 11:37, 11 March 2009 (UTC)

The question is definitely settled. You can see this by clicking on the link to my paper in Terry's comment. This link points to a void page as Terry removed the reference agreeing on the fact that, after my publication in Modern Physics Letters A, mapping theorem, with the proof given in this last paper, is correct. Terry communicated this to me by email. On the other side, I guess that Terry would not agree to push further this matter and I will not put back removed material in this site (or elsewhere other than my blog or peer-reviewed journals) until him or Jim Colliander will ask for this. I take this chance to thank him for providing me the chance to improve my work.--Jonlester 09:42, 15 November 2009 (UTC)

- Just to clarify: the new mapping theorem in the Phys. Lett. A. paper is not the same as the theorem claimed in the earlier reference, as the new theorem is only asymptotic (up to first order expansion only) rather than exact (and indeed, the later paper acknowledges that the exact mapping theorem was, in fact, false). As long as this distinction is made clear, I consider the matter settled. Terry 23:01, 27 November 2009 (UTC)

- Terry, I agree. Sorry if I was not so clear in my intervention. Thank you again.--Jonlester 11:45, 28 November 2009 (UTC)