In physically motivated models of quantum spacetime, a $\mathcal{U}(1)$ gauge theory turns into a $\mathcal{U}(\infty )$ gauge theory; hence, free classical electrodynamics is no longer free and neutral fields may have electromagnetic interactions. We discuss the last point for scalar fields, as a way to possibly describe dark matter; we have in mind the gravitational collapse of binary systems or future applications to self-gravitating Bose-Einstein condensates as possible sources of evidence of quantum gravitational phenomena. The effects considered so far, however, seem too faint to be detectable at present.

• Received 29 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.065009