  Recent work by Elder, Ward and Zhang [Phys. Rev. B83. 165210 (2011)] has
shown need for correction and modification of current implementation of the k.p
method and operator ordering scheme using the interaction parameters defined
under double group consideration. This manuscript examines the difference in
treatment of spin-orbit interaction under the single and double group
formulations. We show that the restriction to the adapted double group bases,
brought about by the imposition of single group selection rule in calculating
the k.p interaction, is not appropriate. In addition, the unitary
transformation employed in the literature to diagonalise the intra-band spin
orbit interaction in semiconductors with diamond lattice can not remove the
inter-band terms. It leads to a bases set for valence band ordered differently
from D_3/2^+ in the O(3) group thus invalidating any correlation of magnetic
quantum number to the z component of angular momentum. Under the double group
consideration, spin-orbit interaction affects all the zone centre states and
offers a mechanism for changing the relative positions of various zone centre
states in the conduction band. In addition to the mixing caused by k
independent spin orbit terms, formation of hybridised orbitals under double
group rules also produce mixing. This can lead to inversion in materials such
as \alpha-tin. The re-arrangement of conduction band zone centre states leads
to a negative \gamma_2 in most materials with respect to the valence band bases
having the same order as D_3/2^+ in the O(3) group. The double group
formulation is also required in the description of Zeeman interaction,
including the S.B term, for the mixed zone centre states. It provides a
correspondence between second order interaction parameters and the Luttinger
invariants. ...
