Gauge Parameterization of the n-Field

Abstract

We propose a gauge parameterization of the three-dimensional n-field using an orthogonal \(\mathbb{SO}(3)\)-matrix, which, in turn, is defined by a field taking values in the Lie algebra so(3) (rotation-angle field). The rotation-angle field has an additional degree of freedom, which corresponds to the gauge degree of freedom of rotations around the n-field. As a result, we obtain a gauge model with local \(\mathbb{SO}(2) \simeq \mathbb{U}(1)\) symmetry that does not contain a \(\mathbb{U}(1)\) gauge field.