to incorporate the other discrete degrees of freedom present, and that the time evolution of these operators can be derived from applying the Heisenberg equation of motion to the MF potential. Finally, we show that the Kubo expression for non equilibrium expectation of spin$\otimes$pseudospin quantities can be interpreted as the first order time independent perturbation theory response to the MF potential.

We then move on to apply the MF potential formalism to study the emergence of a TI thin film system subjected to an in-plane magnetization and electric field. We first illustrate the effects of the interlayer coupling on the in-plane magnetization and the dispersion relations. We then show that the direction of the out of plane spin accumulation resulting from an in-plane electric field can be explained in terms of how the direction of the momentum dependent in-plane SOI field rotates with the change in momentum direction resulting from the electric field. The anti-symmetry of the out of plane spin accumulation in $k$ space can be broken with the application of an out of plane electric field in order to yield a finite spin accumulation after integrating over the Fermi surface.

Spin 1/2 systems {#spinhalf}
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To familarize the 