Talk:Yang-Mills equations: Difference between revisions
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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. [[User:Tao|Terry]] 20:12, 28 February 2009 (UTC) | 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. [[User:Tao|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. --[[User:Jonlester|Jonlester]] 19:32, 10 March 2009 (UTC) | |||
Revision as of 19:32, 10 March 2009
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)
