Abstract
The authors of the article [M. Hirayama, C.-G. Shi, Phys. Lett. B 652 (2007) 384, arXiv: 0707.2207] propose an interesting method to solve the Faddeev model by reducing it to a set of first order PDEs. They first construct a vectorial quantity α, depending on the original field and its first derivatives, in terms of which the field equations reduce to a linear first order equation. Then they find vectors α1 and α2 which identically obey this linear first order equation. The last step consists in the identification of the αi with the original α as a function of the original field. Unfortunately, the authors overlook a constraint implied by their construction, which invalidates most of their subsequent results.
Highlights
In the sequel we briefly review the construction of [8], point out the error and demonstrate that from their results, incorrect conclusions may be drawn
The result essentially says that there are six real functions (the three functions γ, ξ and η, as well as three more functions called a, b and c, which are related to the arbitrary complex functions ρ and μ of Eq (8)), which have to obey a system of two linear first order PDEs (Eq (54) of Ref. [8])
Any choice of these six functions obeying the two linear first order PDEs automatically provides a static solution for the Faddeev model
Summary
In the sequel we briefly review the construction of [8], point out the error and demonstrate that from their (incorrect) results, incorrect conclusions may be drawn (i.e., one may construct “solutions” which are well-known not to be solutions of the Faddeev model). The energy functional for static configurations of the Faddeev model (in terms of the complex field u) is Equation (5) is the starting point for the analysis in Ref.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
