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The consistency condition of the Faddeev-Niemi ansatz for the gauge-fixed massless SU(2) gauge field is discussed. The generality of the ansatz is demonstrated by obtaining a sufficient condition for the existence of the three-component field introduced by Faddeev and Niemi. It is also shown that the consistency conditions determine this three-component field as a functional of two arbitrary functions. The consistency conditions corresponding to the Periwal ansatz for the SU(N ) gauge field with N ≥ 3 are also obtained. It is shown that the gauge field obeying the Periwal ansatz must satisfy extra (N − 1)(N − 2)/2 conditions. by guest on April 10, 2015

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