A theory of the Zeeman effect for electrons in one- and zero-dimension
al semiconductor heterostructures is developed. A relation is establis
hed between the number of linearly independent components of the g-fac
tor tensor and the point symmetry of a low-dimensional system. A speci
fic calculation is performed for a spherical quantum dot and a cylindr
ical wire. (C) 1998 American Institute of Physics. [S0021-3640(98)0080
1-9].