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.

See also

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]


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.