  When an electron or hole is in a conduction band of a crystal, it can be very
different from 2, depending upon the crystalline anisotropy and the direction
of the applied magnetic induction ${\bf B}$. In fact, it can even be 0! To
demonstrate this quantitatively, the Dirac equation is extended for a
relativistic electron or hole in an orthorhombically-anisotropic conduction
band with effective masses $m_j$ for $j=1,2,3$ with geometric mean
$m_g=(m_1m_2m_3)^{1/3}$. The appropriate Foldy-Wouthuysen transformations are
extended to evaluate the non-relativistic Hamiltonian to $O({\rm m}c^2)^{-4}$,
where ${\rm m}c^2$ is the particle's Einstein rest energy. For ${\bf
B}||\hat{\bf e}_{\mu}$, the Zeeman $g_{\mu}$ factor is $2{\rm
m}\sqrt{m_{\mu}}/m_g^{3/2} + O({\rm m}c^2)^{-2}$. While propagating in a
two-dimensional (2D) conduction band with $m_3\gg m_1,m_2$, $g_{||}<<2$,
consistent with recent measurements of the temperature $T$ dependence of the
parallel upper critical induction $B_{c2,||}(T)$ in superconducting monolayer
NbSe$_2$ and in twisted bilayer graphene. While a particle is in its conduction
band of an atomically thin one-dimensional metallic chain along $\hat{\bf
e}_{\mu}$, $g<<2$ for all ${\bf B}={\bf\nabla}\times{\bf A}$ directions and
vanishingly small for ${\bf B}||\hat{\bf e}_{\mu}$. The quantum spin Hall
Hamiltonian for 2D metals with $m_1=m_2=m_{||}$ is $K[{\bf E}\times({\bf
p}-q{\bf A})]_{\perp}\sigma_{\perp}+O({\rm m}c^2)^{-4}$, where ${\bf E}$ and
${\bf p}-q{\bf A}$ are the planar electric field and gauge-invariant momentum,
$q=\mp|e|$ is the particle's charge, $\sigma_{\perp}$ is the Pauli matrix
normal to the layer, $K=\pm\mu_B/(2m_{||}c^2)$, and $\mu_B$ is the Bohr
magneton.
