Gauge parameterization of the $n$-field

We propose gauge parameterization of the three-dimensional $n$-field using orthogonal SO(3)-matrix which, in turn, is defined by a field taking values in the Lie algebra so(3) (rotational-angle field). The rotational-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 SO(2)=U(1) symmetry that does not contain a U(1) gauge field.

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