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 Tr. Mat. Inst. Steklova, 2019, Volume 306, Pages 139–147 (Mi tm4019)

Gauge Parameterization of the $n$-Field

M. O. Katanaevab

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b N. I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, ul. Kremlevskaya 35, Kazan, 420008 Russia

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 $\mathfrak {so}(3)$ (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.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation The work was supported in part by the Russian Government Program of Competitive Growth of Kazan Federal University (Russian Academic Excellence Project “5-100”).

DOI: https://doi.org/10.4213/tm4019

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 306, 127–134

Bibliographic databases:

UDC: 530.21
Revised: May 10, 2019
Accepted: May 10, 2019

Citation: M. O. Katanaev, “Gauge Parameterization of the $n$-Field”, Mathematical physics and applications, Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 306, Steklov Math. Inst. RAS, Moscow, 2019, 139–147; Proc. Steklov Inst. Math., 306 (2019), 127–134

Citation in format AMSBIB
\Bibitem{Kat19} \by M.~O.~Katanaev \paper Gauge Parameterization of the $n$-Field \inbook Mathematical physics and applications \bookinfo Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov \serial Tr. Mat. Inst. Steklova \yr 2019 \vol 306 \pages 139--147 \publ Steklov Math. Inst. RAS \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm4019} \crossref{https://doi.org/10.4213/tm4019} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4040771} \transl \jour Proc. Steklov Inst. Math. \yr 2019 \vol 306 \pages 127--134 \crossref{https://doi.org/10.1134/S0081543819050122} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077365318}