A Poincaré gauge theory of gravity
The author proposes a new gauge theory of gravity with gauge group the covering group \(\overline{P}_ 0\) of the proper orthochronous Poincaré group. The mathematical language used is that of a principal fibre bundle over spacetime. In addition to the geometrical fields which are constructed from the connection, the theory includes a Higgs-type field and a matter field. The base manifold of the bundle, the spacetime, acquires a Lorentzian metric and a spinor structure, resulting from the geometrical and the Higgs field, respectively. An action is proposed and the associated Lagrangian depends on the fields and their first derivatives. The conservation laws implied by the gauge symmetry are investigated. It is shown that one can also consider ''intrinsic'' energy and momentum, arising from the invariance of the theory along the intrinsic translational degrees of gauge freedom. When the intrinsic energy-momentum of the matter fields vanishes the proposed theory agrees, for all practical reasons, with the conventional Poincaré gauge theory of gravity.
scientific article; zbMATH DE number 3971701