Towards a third-order topological invariant for magnetic fields

被引:20
作者
Hornig, G [1 ]
Mayer, C [1 ]
机构
[1] Ruhr Univ Bochum, Fak Phys & Astron, D-44780 Bochum, Germany
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2002年 / 35卷 / 17期
关键词
D O I
10.1088/0305-4470/35/17/309
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
An expression for a third-order link integral of three magnetic fields is presented. It is a topological invariant and therefore an invariant of ideal magnetohydrodynamics. The integral generalizes existing expressions for third-order invariants which are obtained from the Massey triple product, where the three fields are restricted to isolated flux tubes. The derivation and interpretation of the invariant show a close relationship with the well-known magnetic helicity, which is a second-order topological invariant. Using gauge fields with an SU (2) symmetry, helicity and the new third-order invariant originate from the same identity, an identity which relates the second: Chern class and the Chem-Simons 3-form. We present an explicit example of three magnetic fields with non-disjunct support. These fields, derived from a vacuum Yang-Mills field with a non-vanishing winding number, possess a third-order linkage detected by our invariant.
引用
收藏
页码:3945 / 3959
页数:15
相关论文
共 18 条
[1]  
[Anonymous], 1998, TOPOLOGICAL METHODS
[2]  
Arnold I., 1986, SEL MATH SOV, V5, P327
[3]   3RD-ORDER LINK INTEGRALS [J].
BERGER, MA .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (13) :2787-2793
[4]  
BROWN MR, 1999, GEOPHYSICAL MONOGRAP, V111
[5]   HYDROMAGNETIC DYNAMO THEORY [J].
ELSASSER, WM .
REVIEWS OF MODERN PHYSICS, 1956, 28 (02) :135-163
[6]  
EVANS NW, 1992, NATO ASI SERIES E, V218, P237
[7]  
FENN RA, 1983, LONDON MATH SOC LECT
[8]  
FRANKEL T, 1997, GEOMETRY PHYSICS INT
[9]  
GAUSS CF, 1867, WERKE, V5, P602
[10]  
Itzykson C., 1980, Quantum field theory