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Note: There appears to be a serious error in this paper, in Theorem 1: a field A which is a critical point (or extremiser) for the Yang-Mills functional when restricted to a special subclass of fields, is not necessarily a critical point for the functional for all fields, and in particular is not necessarily a solution to the Yang-Mills equation. | Note: There appears to be a serious error in this paper, in Theorem 1: a field A which is a critical point (or extremiser) for the Yang-Mills functional when restricted to a special subclass of fields, is not necessarily a critical point for the functional for all fields, and in particular is not necessarily a solution to the Yang-Mills equation. | ||
Note 2): There is no error. The class of Smilga's solutions are common both to Yang-Mills equations and scalar field theory and grants an extremum for both. This has been proved in [http://arxiv.org/abs/0903.2357 arxiv:0903.2357 [math-ph]]. For all other cases, solutions are common solutions in the limit <math>g\rightarrow\infty</math>, being <math>g</math> the coupling constant. This is all is needed for the low-energy analysis of Yang-Mills theory. | |||
Revision as of 15:10, 18 May 2009
M. Frasca. Infrared Gluon and Ghost Propagators. Phys. Lett, B670 (2008), 73-77. MathSciNet, arXiv.
Note: There appears to be a serious error in this paper, in Theorem 1: a field A which is a critical point (or extremiser) for the Yang-Mills functional when restricted to a special subclass of fields, is not necessarily a critical point for the functional for all fields, and in particular is not necessarily a solution to the Yang-Mills equation.
Note 2): There is no error. The class of Smilga's solutions are common both to Yang-Mills equations and scalar field theory and grants an extremum for both. This has been proved in arxiv:0903.2357 [math-ph]. For all other cases, solutions are common solutions in the limit , being the coupling constant. This is all is needed for the low-energy analysis of Yang-Mills theory.
