  The one dimensional spin-1/2 Heisenberg antiferromagnet in a weak magnetic
field h is studied using the bosonization method. We derive a set of
renormalization group equations. The fixed point is reached when the field is
scaled to the value at which the system is quarter-filled. As the magnetic
field varies, a continuum line of fixed points is formed. We compute the
uniform longitudinal susceptibility $\chi_z(h)$. The singular behavior of
$\chi_z(h)$ as $h\to 0$ is found to be contained in $1/\ln(h_o/h)$ with $h_o$ a
non-universal constant. The spin-spin correlations in the magnetic field are
calculated.
