  A theoretical study is made of conformal factors in certain types of physical
theories based on classical differential geometry. Analysis of quantum versions
of Weyl's theory suggest that similar field equations should be available in
four, five and more dimensions. Various conformal factors are associated with
the wave functions of source and test particles. This allows for quantum field
equations to be developed. The curvature tensors are calculated and separated
into gravitational, electromagnetic and quantum components. Both four and five
dimensional covariant theories are studied. Nullity of the invariant five
scalar of curvature leads to the Klein-Gordon equation. The mass is associated
with an eigenvalue of the differential operator of the fifth dimension.
Different concepts of interaction are possible and may apply in a quantum
gravitational theory.
