It is shown that a consistent gauging of the Poincaré group is capable of including Einstein's general relativity. This statement holds for matter particles of arbitrary spin, provided the nontrivial part of the vierbein is taken as the fundamental gravitational field, thus giving rise to a known modification of the original theory. Since the gauge approach implies that gravitation is an ordinary field theory over flat space, the standard prescriptions for calculating the asymmetric momentum tensor of both matter and gravitation are available. Applying Belinfante's flat-space symmetrization procedure to the latter, we prove that the symmetrization of the asymmetric matter tensor just gives the dynamically defined symmetric matter tensor, whereas the symmetrization of the asymmetric gravitational momentum tensor leads to another version of the field equations that reveals a deep analogy to the equations of electrodynamics. Furthermore a method is developed that admits an unambiguous calculation of gauge-fixing conditions from a given gauge-breaking term. Besides the harmonic gauge, which can be reproduced by means of this method, new gauge-fixing conditions for local translations and local Lorentz transformations are obtained. These gauge-fixing techniques, as well as the symmetrization procedure, may equally be generalized to the case of nonvanishing torsion.

• Received 17 February 1982

DOI:https://doi.org/10.1103/PhysRevD.28.286