Gianluca Calcagni, Giuseppe Nardelli
The symmetries of a scalar field theory in multi-fractional 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.
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http://arxiv.org/abs/1210.2754
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