Gauge fields arising from spacetime symmetries and gravitational theories. I

Abstract

The Utiyama method of obtaining an interaction from an invariance principle is applied in the case of external (spacetime) symmetries. The "gauge" fields arising from a spacetime symmetry with respect to a general $N$-parameter Lie group are introduced following Kibble's extension. The corresponding formulas are obtained, which are more general than Kibble's and are reduced to Kibble's if we identify the generic $N$-parameter group with the Poincar\'e 10-parameter group.