  Correlation functions (CFs) of the classical Heisenberg antiferromagnet on
the pyrochlore lattice are studied by solving exactly the infinite-component
spin-vector model. % As in many Fully Frustrated Lattices, the constraint due
to the minimization of the energy and the particular structure based on corner
sharing tetrahedra both contribute to the creation of local degrees of freedom.
% The resulting degeneracy destroys any magnetic order at all temperature and
we obtain no sign of criticality, even at $T = 0$. % Calculated neutron
scattering cross sections have their maxima beyond the first Brillouin Zone and
reproduce experimental results obtained on Y(Sc)Mn$_2$ and CsCrNiF$_6$ as well
as theoretical predictions previously obtained by classical Monte Carlo
simulations. % Evidences for thermal and spatial decoupling of the magnetic
modes are found so that the magnetic fluctuations in this system can be
approximated by $S(q,T) \approx f(q) h(T)$.
