Weyl Transformations and Poincare Gauge lnvariance

Invariance under Weyl transformations of a scale and Poincare gauge invariant matter lagrangian is established ·by introducing a minimally coupled vector gauge field, r/Jp., and a Weyl invariant modified spin gauge field, Ak!p. · The identities governing the corresponding modified matter lagrangian are derived in a form that is manifestly covariant under both Weyl and Poincare gauge transformations. In particular it is shown that the covariant divergence of the energy-momentum tensor is proportional to a set of Lorentz force type terms, i.e., to products of the various gauge field currents and the corresponding gauge invariant field-strengths ~ The case that the field r/Jp. is related to the derivative of a scalar field is examined; it is found that use of the simplest possible free lagrangians for the various fields leads to a modification of the Brans-Dicke theory (in its singular version where the Brans-Dicke parameter w has the value- (3/2)) corresponding to the presence of torsion and an asym-metric energy-momentum tensor. § I. Introduction and summary The W eyl unified field theory of 19181l · 2l can be considered the prototype of all subsequent gauge theories; indeed the idea of "gauge " invariance in Physic