A GLOBAL FORMULATION FOR GRAVITATION

Abstract

The teleparallel equivalent of general relativity,1 or teleparallel gravity for short,2 can be understood as a gauge theory for the translation group.3 According to this theory, the fundamental field describing gravitation is the translational gauge potential*1 Ban, a 1-form assuming values in the Lie algebra of the translation group.4 By using the analogy with the electromagnetic gauge potential A^, a gravitational nonintegrable phase-factor can thus be defined. The translational gauge invariant action of this phase-factor gives rise to a teleparallel global formulation for gravitation. The global formulation of electromagnetism, which consists in the U{\) gauge invariant action of a nonintegrable (path-dependent) phase factor, is quite well known.5 For a particle with electric charge e traveling from an initial point P to a final point Q, the phase factor is given by