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

TL;DR

This paper examines the consistency conditions of the Faddeev-Niemi and Periwal ansatzes for SU(N) gauge fields, establishing criteria for their validity and expressing the fields as functionals of arbitrary functions.

Contribution

It extends the analysis of the Faddeev-Niemi ansatz to SU(N) gauge fields, deriving new consistency conditions and showing how the fields depend on arbitrary functions.

Findings

The Faddeev-Niemi ansatz's generality is demonstrated for SU(2).

Consistency conditions determine the three-component field as a functional of two functions.

Additional conditions are required for the Periwal ansatz when N > 2.

Abstract

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.