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 Tr. Mat. Inst. Steklova, Forthcoming paper (Mi tm4019)

Gauge parameterization of $n$-field

M. O. Katanaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We propose gauge parameterization of the three-dimensional $n$-field using orthogonal $\mathbb S\mathbb O(3)$-matrix which, in its turn, is defined by the field taking values in the Lie algebra $\mathfrak{s}\mathfrak{o}(3)$ (rotational angle field). The rotational angle field has one more degree of freedom which corresponds to the gauge degree of freedom of rotations around the $n$-field. As the consequence we obtain gauge model with local $\mathbb S\mathbb O(2)\simeq\mathbb U(1)$ symmetry which does not contain $\mathbb U(1)$ gauge field.

Document Type: Article
UDC: 530.21