A Hodge dual for soldered bundles

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.