AN EXTENDED NEW GENERAL-RELATIVITY AS A REDUCTION OF POINCARE GAUGE-THEORY OF GRAVITY - GENERATORS OF INTERNAL AND COORDINATE TRANSFORMATIONS

An extended new general relativity (E. N. G. R.) is formulated as a reduction of activated Poincare gauge theory (PBAR. G. T.) of gravity whose gauge group is the covering group of the Poincare group. Fundamental fields in the theory are a Higgs-type field psi-k, and the translational gauge potential A(k)-mu and a matter field phi-a. The components e(k)-mu of the duals of the vierbein fields are given by e(k)-mu = nabla-mu*psi-k = psi-k, mu + A(k)-mu. Internal translation an the field psi-k, which the conventional new general relativity lacks, play fundamental roles in E. N. G. R. as well as in PBAR. G. T. The restrictions on the Lagrangian density, identities and differential conservation laws following from the (local internal translation x global SL(2, C)) x general coordinate transformations are given. For the specific gravitational Lagrangian L(T) = - (1/3K)t(klm)t(klm) + (1/3K)-upsilon-k-upsilon-k + a3a(k)a(k), the generators of internal activated Poincare and general affine coordinate transformations isolated system are examined. The results are quite parallel to those in PBAR. G. T., but the former is not trivial reductions of the latter. The following is worth noticing also in E. N. G. R.: For the case in which {psi-k, A(k)-mu, phi-a} with psi-k congruent-to e(o)k-mu-y-mu + psi-(o)k is employed as the set of independent variables, (a) the generators of (internal translation x SL(2, C)) give the energy-momentum and the total angular momentum for an isolated system, and (b) the generators of general affine coordinate transformations vanish and are trivial.