Symmetries and propagator in multifractional scalar field theory

The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincaré algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In the interacting case, the Poincaré 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.

Figure 1

Top panel: The nonfactorizable measure $v_{\mathrm{diag}}$ [Eq. (18), bottom surface] and the factorizable one $v_{*}$ [Eq. (19), top surface] for $D=2$, ${\alpha }_1=1/2$ and ${\alpha }_2=1$. Bottom panel: The difference $\Delta v=v_{*}-v_{\mathrm{diag}}$. Gamma factors have been omitted.