In Sec. \[sec:II\] we consider, as a warm-up and to introduce various concepts, classical magnets, and show how the vector potential coupling to the magnetization gives rise to the dipole-dipole interaction. In Sec. \[sec:III\] we develop the technical machinery for dealing with quantum magnets and provide the derivations mentioned above. In Sec. \[sec:IV\] we discuss our results and provide a summary and conclusion. Some technical details are relegated to various appendices.

Effective Action for Classical Ferromagnets and Helimagnets {#sec:II}
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We now proceed to derive an effective action for magnets that includes the effects of the fluctuating electromagnetic potential. We first consider the classical case as a warm-up; we will generalize to the quantum case in Sec.\[sec:III\].

Dipole-dipole interaction {#subsubsec:II.A}
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Consider a classical model for a ferromagnet with a three-component order parameter ${\bm M}$. In addition to the field ${\bm M}({\bm x})$ we need to consider the electromagnetic vector potential ${\bm A}({\bm x})$, and the partition function $Z$ is given by \[eqs:2.1\] Z &=& D\[[M]{},[A]{}\] e\^[S\[[M]{},[A]{}\]]{} \[eq:2.1a\]\
&& D\[[M]{}\] e\^[-[F]{}\[[M]{}\]/T]{}. \[eq:2.1b\] The model is defined by specifying the action $S$, and in Eq. (\[eq:2.1b\]) we have anticipated integrating out the vector potential to obtain an effective action ${\cal F}$ 