  Finite quantum field theories may be constructed from the most general
renormalizable quantum field theory by forbidding, order by order in the
perturbative loop expansion, all ultraviolet-divergent renormalizations of the
physical parameters of the theory. The relevant finiteness conditions resulting
from this requirement relate all dimensionless couplings in the theory. At
first sight, Yukawa couplings which are equivalent to the generators of some
Clifford algebra with identity element represent a very promising type of
solutions of the condition for one-loop finiteness of the Yukawa couplings.
However, under few reasonable and simplifying assumptions about their
particular structure, these Clifford-like Yukawa couplings prove to be in
conflict with the requirements of one- and two-loop finiteness of the gauge
coupling and of the absence of gauge anomalies, at least for all simple gauge
groups up to and including rank 8.
