Consistency Conditions of the Faddeev-Niemi-Periwal Ansatz for the SU(N) Gauge Field

M. Hirayama, M. Kanno, M. Ueno, H. Yamakoshi

Published 1998-12-21, updated 1999-04-16Version 3

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 larger than 2 are also obtained. It is shown that the gauge field obeying the Periwal ansatz must satisfy extra (N-1)(N-2)/2 conditions.