T4 gauge theory of gravity and new general relativity

Abstract

We formulate a space-time translationT4 gauge theory of gravity on the Minkowski space-time with appropriate choice of the Lagrangian. By comparing the energy-momentum law of this theory with that of new general relativity constructed on the Weitzenbock space-time we find that in the classical limit the gauge potentials correspond to the parallel vector fields in the Weitzenbock space-time and the gauge field equation coincides with the field equation of gravity in new general relativity in the linearized version. Thus we conclude that in the classical limit theT4 gauge theory of gravity leads to the new general relativity.