Group actions on principal bundles and dimensional reduction

• DOI: 10.1007/bf00417502
• Publication Date: 2004-11-09T16:38:42Z
• Authors: J. Harnad; S. Shnider; J. Tafel
• Keywords: 0101 mathematics; 01 natural sciences

Using the invariant geometrical interpretation of gauge and Higgs fields, a simple derivation is given of the dimensional reduction procedure. The underlying assumption with regard to the Riemannian structure, group orbits and invariant connection are clarified and the critical points of the Higgs potential are shown to have a natural geometrical interpretation.