The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the fl
For example,a reasonable lowest-order approximation of the RHS of Eq.
(B.8)
is
given by its local limit,K C (M C )?1K C =(n ·?λn ×?λµn )
1(2π)4p λp κp µp ν
31k δλκδµν+δλµδκν+δλνδκµ .(C.10)
From this formula,we can also deduce upon index contraction that
[k,Λ]d 4p p 6=1k , [k,Λ]d 4p p 4
=1k .(C.11)
The last integral is,of course,standard and can be used to prove Eq.(C.10)in addition to symmetry arguments.The same philosophy applies to the second type of integrals:
[k,Λ]
d 4p p 4=1(2π)4116π
2(Λ2?k 2).(C.12)References
[1]L.Faddeev and A.J.Niemi,Phys.Rev.Lett.82,1624(1999)[hep-th/9807069].
[2]Y.M.Cho,Phys.Rev.D21,1080(1980);Phys.Rev.D23,2415(1981).
[3]V.Periwal,hep-th/9808127.
[4]L.Faddeev and A.J.Niemi,Phys.Lett.B449,214(1999)[hep-th/9812090].
[5]ngmann and A.J.Niemi,Phys.Lett.B463,252(1999)[hep-th/9905147].
[6]Y.M.Cho,H.Lee and D.G.Pak,hep-th/9905215.
[7]L.Faddeev and A.J.Niemi,hep-th/0101078.
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