Hodge Dual for Soldered Bundles
arXiv:0811.2066 · doi:10.1088/1751-8113/42/3/035402
Abstract
In order to account for all possible contractions allowed by the presence of the solder form, a generalized Hodge dual is defined for the case of soldered bundles. Although for curvature the generalized dual coincides with the usual one, for torsion it gives a completely new dual definition. Starting from the standard form of a gauge lagrangian for the translation group, the generalized Hodge dual yields precisely the lagrangian of the teleparallel equivalent of general relativity, and consequently also the Einstein-Hilbert lagrangian of general relativity.
8 pages, no figures. Accepted for publication in Journal of Physics A