We now turn to a quantum mechanical description of itinerant fermion systems in general, and certain types of magnetism in particular. We will show how the exchange interaction, the dipole-dipole interaction, and the DM interaction naturally arise in the context of a field-theoretic description of itinerant electrons. The former two lead to ferromagnetism, and the latter, if it is present, to helimagnetism.

Action {#subsec:III.A}
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In Appendix \[app:A\] we list the complete action for free quasi-relativistic electrons, to order $1/c^2$, coupled to the electromagnetic field. Several terms in the complete action are not relevant for our present purposes. The only effect of the Darwin term, Eq. (\[eq:A.4g\]), is to modify the Coulomb interaction on length scales given by the electronic Compton wave length $\lambdae = 1/\me c$. The relativistic mass enhancement, the last term in Eq.(\[eq:A.4b\]), is a higher-order gradient term that is small compared to terms of the same form that are generated by renormalizing the final effective action. Finally, the Landau diamagnetic terms, Eq. (\[eq:A.4f\]), give rise to diamagnetism and, in the presence of an external magnetic field, Landau levels. These effects are physically very different from ferromagnetism or helimagnetism, and we do not consider them here. Finally, 