  The effect of magnetic field on the static and dynamic spin correlations in
the non-centrosymmetric heavy-fermion superconductor CePt$_3$Si was
investigated by neutron scattering. The application of a magnetic field B
increases the antiferromagnetic (AFM) peak intensity. This increase depends
strongly on the field direction: for B${\parallel}$[0 0 1] the intensity
increases by a factor of 4.6 at a field of 6.6 T, which corresponds to more
than a doubling of the AFM moment, while the moment increases by only 10 % for
B${\parallel}$[1 0 0] at 5 T. This is in strong contrast to the inelastic
response near the antiferromagnetic ordering vector, where no marked field
variations are observed for B${\parallel}$[0 0 1] up to 3.8 T. The results
reveal that the AFM state in CePt$_3$Si, which coexists with superconductivity,
is distinctly different from other unconventional superconductors.
