Geodesic
Gauge Parameterization of the $n$-Field
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 139-147

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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 $\mathfrak {so}(3)$ (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. 
@article{TM_2019_306_a11,
     author = {M. O. Katanaev},
     title = {Gauge {Parameterization} of the $n${-Field}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {139--147},
     publisher = {mathdoc},
     volume = {306},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_306_a11/}
}
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M. O. Katanaev. Gauge Parameterization of the $n$-Field. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 139-147. http://geodesic.mathdoc.fr/item/TM_2019_306_a11/