  The S=1/2 antiferromagnetic Heisenberg chain exhibits a magnetic field driven
quantum critical point. We study the low frequency spin dynamics in copper
pyrazine dinitrate (CuPzN), a realization of this model system of quantum
magnetism, by means of $^{13}$C-NMR spectroscopy. Measurements of the nuclear
spin-lattice relaxation rate $T_1^{-1}$ in the vicinity of the saturation field
are compared with quantum Monte Carlo calculations of the dynamic structure
factor. Both show a strong divergence of low energy excitations at temperatures
in the quantum regime. The analysis of the anisotropic $T_1^{-1}$-rates and
frequency shifts allows one to disentangle the contributions from transverse
and longitudinal spin fluctuations for a selective study and to determine the
transfer of delocalized spin moments from copper to the neighboring nitrogen
atoms.
