  Large neutrino mixing angles suggest that the Yukawa sector is invariant
under permutations of the fermion families. This S_{3} permutation symmetry is
broken at a large energy scale but much below the unification scale. Assuming
that the lepton mass matrix is approximately diagonal, all neutrino mixing
angles naturally come from the breaking of S_{3}-> S_{2}. In the neutrino
sector, S_{2} remains (approximately) unbroken. As a consequence, we have a
large atmospheric neutrino angle and U_{e3}=0. The S_{3} symmetry at the
unification scale can also explain the large solar mixing angle. We give an
explicit expression of the solar mixing angle in terms of the left-handed
neutrino masses. We observe that this family permutation symmetry comes very
naturally from a quantized theory of functionals [1], that is an extension of
quantum field theory.
