  Conformal symmetry is investigated within the context of
axion-dilaton-modulus theory of gravity of Brans-Dicke-type. A distinction is
made between general conformal symmetry and invariance under transformations of
the physical units. The conformal degree of symmetry of the theory is studied
when quantum fermion (lepton) modes with electromagnetic interaction are
considered. Based on the requirement of invariance of the physical laws under
general transformations of the units of measure, arguments are given that point
at a matter action with non-minimal coupling of the dilaton to the matter
fields as the most viable description of the world within the context of the
model studied. The geometrical implications of the results obtained are
discussed.
