We find and characterize the instabilities of the repulsive Hubbard ch
ain in a magnetic field by studying all response functions at low freq
uency omega and arbitrary momentum. The instabilities occur at momenta
which are simple combinations of the (U=0) sigma = up arrow,down arro
w Fermi points, +/-k(F sigma). For finite values of the on-site repuls
ion U the instabilities occur for single a electron added or removed a
t momenta +/- k(F sigma), for transverse spin-density wave (SDW) at mo
menta +/- 2k(F) (when 2k(F)=k(F up arrow) + k(F down arrow)) and for a
charge-density wave and SDW at momenta +/- 2k(F up arrow) and +/- 2k(
F down arrow). While removing or adding single electrons is dominant a
t zero magnetic field, the presence of that field brings about a domin
ance for the transverse +/-2k(F) SDW over all the remaining instabilit
ies for a large domain of U and density n values. We go beyond conform
al-field theory and study divergences which occur at finite frequency
in the one-electron Green function at half-filling and in the transver
se-spin response function in the fully polarized ferromagnetic phase.