Bogomolny equations
In mathematics, and especially gauge theory, the Bogomolny equations for magnetic monopoles are the equations FA = *DAφ, where FA 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.
References
- Hitchin, N. J. (1982), "Monopoles and geodesics", Communications in Mathematical Physics, 83 (4): 579–602, doi:10.1007/bf01208717, ISSN 0010-3616, MR 0649818
- "Magnetic_monopole", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
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