and magnetic components of the antisymmetric 2-tensor $Q^{\mu\nu}$. In the next section we will give some numerical estimates on the electromagnetic radiation and on the perturbations of the motion of charged particles associated to such a magnetic moment in suitable astrophysical situations.

Some potentially observable consequences
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Defining, as usual, the free scalar field on QST as [@DFR] $$\ph(q) = \int_{\bR^3} \frac{d{{\boldsymbol{k}}}}{\sqrt{\om({{\boldsymbol{k}}})}} [a({{\boldsymbol{k}}})\otimes e^{-ikq}+a({{\boldsymbol{k}}})^*\otimes e^{ikq}],$$ and specializing to a point in the spectrum of the $Q$’s, where $\boldsymbol{e} =\boldsymbol{m}$, a computation yields the following expression for the total magnetic moment  $$\begin{split}
{\boldsymbol{M}}(t) = \frac{e\la_P^2}{2}\int_{\bR^3} \frac{d{{\boldsymbol{k}}}}{\om({{\boldsymbol{k}}})}&\left\{ \left[a(-{{\boldsymbol{k}}})a({{\boldsymbol{k}}}) e^{-2i\om({{\boldsymbol{k}}})t}+a({{\boldsymbol{k}}})^*a(-{{\boldsymbol{k}}})^* e^{2i\om({{\boldsymbol{k}}})t}\right] \cos(\om({{\boldsymbol{k}}}){\boldsymbol{e}}\cdot{{\boldsymbol{k}}}){{\boldsymbol{k}}}^2 {\boldsymbol{e}}^\perp\right.\\
&\quad+\left.2a({{\boldsymbol{k}}})^*a({{\boldsymbol{k}}})[2\om({{\boldsymbol{k}}}){{\boldsymbol{k}}}\wedge {\boldsymbol{e}}+ {{\boldsymbol{k}}}^2 {\boldsymbol{e}}^\perp]\right\},
\end{split}$$ with ${\boldsymbol{e}}^\perp = {\boldsymbol{e}}- ({{\boldsymbol{k}}}\cdot{\boldsymbol{e}}){{\boldsymbol{k}}}/{{\boldsymbol{k}}}^2$ the component of ${\boldsymbol{e}}$ orthogonal to ${{\boldsymbol{k}}}$. Therefore the effective magnetic moment of a particle with sharp momentum ${{\boldsymbol{k}}}$ is given by $$\label{eq:momentsharp}
{\boldsymbol{\mu}}_{{\boldsymbol{e}},{{\boldsymbol{k}}}} = e\la_P^2\left[2{{\boldsymbol{k}}}\wedge {\boldsymbol{e}}+ \frac{{{\boldsymbol{k}}}^2}{\om({{\boldsymbol{k}}})} {\boldsymbol{e}}^\perp\right].$$

Of course detectable effects, if any, of the above interaction can be obtained in situations which give rise to a very large magnetic moment. To this end, it is natural to consider a compact “star” of $\ph$ particles in rapid rotation around a very massive companion, akin to a binary pulsar or black hole. Neglecting the rotation of this star around 