Dimensionality of the Zeeman energy in conductors

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=(m₁m₂m₃)^1/3. Its covariance is established with general proper and improper Lorentz transformations. The non-relativistic Hamiltonian is evaluated to order 1/(mc²)⁴, where mc² is it's Einstein rest energy. For the magnetic induction B in the crystallographic direction ê_j, the Zeeman g factor is 2m(m_j/m_g³)^1/2. While propagating in a monolayer two-dimensional conduction band, g is much less than 2 for B parallel to the monolayer, as observed recently in superconducting monolayer NbSe₂, B_c2,|| of which appears to violate the ``Pauli limit'' by a order of magnitude. In one-dimensional chain conductors of atomic thickness, g is small for all B directions.while the particle is in its conduction band. The precise form for the quantum spin Hall energy is also found for a particle in a two-dimensional metal.