Weyl Transformations and Poincaré Gauge Invariance

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Abstract
Invariance under Weyl transformations of a scale and Poincaré gauge invariant matter lagrangian is established by introducing a minimally coupled vector gauge field, φµ, and a Weyl invariant modified spin gauge field, \hatAklµ. the identities governing the corresponding modified matter lagrangian are derived in a form that is manifestly covariant under both Weyl and Poincaré 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 φµ 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 ω has the value -(3/2)) corresponding to the presence of torsion and an asymmetric energy-momentum tensor.

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