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Concept
Bogomolny equations
Summary
In mathematics, and especially gauge theory, the Bogomolny equation for magnetic monopoles is the equation
where is the curvature of a connection on a principal -bundle over a 3-manifold , is a section of the corresponding adjoint bundle, is the exterior covariant derivative induced by on the adjoint bundle, and is the Hodge star operator on . These equations are named after E. B. Bogomolny and were studied extensively by Michael Atiyah and Nigel Hitchin.
The equations are a dimensional reduction of the self-dual Yang–Mills equations from four dimensions to three dimensions, and correspond to global minima of the appropriate action. If is closed, there are only trivial (i.e. flat) solutions.
Official source
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