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
Integrating out the hard modes A H results in two determinants in one-loop approximation,Γk[A S]=
1
α
?? µν A=A S,(20)
where Dµdenotes the covariant derivative and Fµνthe?eld strength tensor.The explicit representation of Eq.(20)in terms of the n?eld is again given in App.A,Eqs.(A.6) and(A.7).The determinants in Eq.(19)can be calculated in a derivative expansion in the same way as described in the preceding section.Since the computation of the term ～(?n)2is already very laborious,we do not calculate the marginal terms～(?µn×?νn)2 etc.directly,but take over the known one-loop results for the running coupling and the gauge parameter from[11].The?nal result for the Wilsonian one-loop e?ective action for the soft modes of the n?eld reads
Γk[n]=
Λ2
4 131
2 1312
131 3
1