Einstein Lagrangian as the translational Yang-Mills Lagrangian

Abstract

The gauge theory of translation with a Yang-Mills-type Lagrangian quadratic in the field strengths is shown to be precisely Einstein's theory of gravitation and the corresponding gauge transformation is identified as the general coordinate transformation. The gauge potentials of the translation group are interpreted as the nontrivial part of the vierbein fields and the gauge field strengths are given in terms of the anholonomity of the local orthonormal basis one starts with.