  The symmetries of a scalar field theory in multifractional spacetimes are
analyzed. The free theory realizes the Poincar\'e algebra, and the associated
symmetries are modifications of ordinary translations and Lorentz
transformations. In the interacting case, the Poincar\'e algebra is broken by
interaction terms. The Feynman propagator of the scalar field is computed and
found to possess the usual mass poles. As a consequence of these findings, the
mass of a particle is a well-defined concept at all scales, and a perturbative
quantum theory can be constructed.
