Gauge Parameterization of the n-Field

Abstract

© 2019, Pleiades Publishing, Ltd. We propose a gauge parameterization of the three-dimensional n-field using an orthogonal 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 SO(2) ≃ U(1) symmetry that does not contain a U(1) gauge field.