  The long-range proximity effect in superconductor/ferromagnet (S/F) hybrid
nano-structures is observed if singlet Cooper pairs from the superconductor are
converted into triplet pairs which can diffuse into the fer- romagnet over
large distances. It is commonly believed that this happens only in the presence
of magnetic inhomogeneities. We show that there are other sources of the
long-range triplet component (LRTC) of the con- densate and establish general
conditions for their occurrence. As a prototypical example we consider first a
system where the exchange field and spin-orbit coupling can be treated as time
and space components of an effective SU(2) potential. We derive a SU(2)
covariant diffusive equation for the condensate and demonstrate that an
effective SU(2) electric field is responsible for the long-range proximity
effect. Finally, we extend our analysis to a generic ferromagnet and establish
a universal condition for the LRTC. Our results open a new avenue in the search
for such correlations in S/F structures and make a hitherto unknown connection
between the LRTC and Yang-Mills electrostatics.
