Symmetries and propagator in multifractional scalar field theory

TL;DR

This paper investigates the symmetries and propagator of scalar fields in multifractional spacetimes, showing that free theories maintain modified Poincaré symmetries and that a consistent quantum theory with well-defined particle mass can be developed.

Contribution

It provides a detailed analysis of symmetries and propagator behavior in multifractional scalar field theories, highlighting how interactions break symmetries but still allow for a well-defined particle mass.

Findings

Free theory preserves modified Poincaré algebra.

Interaction terms break Poincaré symmetry.

Feynman propagator has standard mass poles.

Abstract

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.