Weyl conjugacy

Two objects are the to be Weyl conjugate if they transform identically under the Lorentz group and have opposite Weyl weights. In this paper, the authors show how the existence of conjugate pairs of fields and operators resolves the problems which historically have prevented conformal invariance from being accorded the status of a fundamental spacetime symmetry. The authors construct the gauge theory of the conformal group which contains conjugate fields that lead to a unique scale-free spacetime metric on the resulting Weyl geometry. The existence of this metric allows a nontrivial Weyl vector to coexist with length- preserving classical measurements and permits the use of Weyl geometry as a model of the physical world