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Bogomolny equations : ウィキペディア英語版
Bogomolny equations
In mathematics, the Bogomolny equations for magnetic monopoles are the equations ''F''''A'' = 
*''D''''A''''φ'', where ''F''''A'' is the curvature of a connection ''A'' on a ''G''-bundle over a 3-manifold ''M'', ''φ'' is a section of the corresponding adjoint bundle and
* is the Hodge star operator on ''M''. These equations are named after E. B. Bogomolny.
The equations are a dimensional reduction of the self-dual Yang–Mills equations in four dimensions and correspond to global minima of the appropriate action. If M is closed there are only trivial (i.e., flat) solutions.
==See also==

*Monopole moduli space

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