  We theoretically study the magnetoresistance of single wall carbon nanotubes
(SWCNTs) in the ballistic transport regime, using a standard tight-binding
approach. The main attention is directed to spin-polarized electrical transport
in the presence of either axial or perpendicular magnetic field. The method
takes into account both Zeeman splitting as well as size and chirality effects.
These factors (along with a broadening of energy levels due to a strong
nanotube/electrode coupling) lead, in ultra small SWCNTs, to serious
modifications in profile of the Aharonov-Bohm oscillations. Other noteworthy
findings are that in the parallel configuration (axial magnetic field) the
ballistic magnetoconductance is negative (positive) for armchair
(semiconducting zigzag) nanotubes, whereas in the perpendicular configuration
the magnetoresistance is nearly zero both for armchair and zigzag SWCNTs.
