NOTE ON CONFORMAL FIELD-EQUATIONS

Conformal geometry is more fundamental than a Riemannian one. Whereas Riemannian geometry determines lengths and angles, a conformal one determines only angles and ratios of length. Equivalently, conformal geometry of space-time determines light cones, or causal structure. No length scale is a priori distinguished. It can be distinguished only a posteriori, given a particular solution of matter field equations. Einstein's field equations of gravitation can be thought of as describing interaction of causal structure with a matter described by a real scalar massless field of weight 1/4. Electromagnetic field equations need precisely a conformal structure. One can also write down field equations for a spin-1/2 Dirac massless field, given information about light cones only. The energy-momentum tensor density is obtained by vierbeim variations. © 1979 Plenum Publishing Corporation.