Anomalousg-Factors for Charged Leptons in a Fractional Coarse-Grained Approach

Abstract

We here propose to extend the concept of helicity to include it in a fractional scenario and we write down the left- and the right-handed Weyl equations from first principles in this extended framework. Next, by coupling the different fractional Weyl sectors by means of a mass parameter, we arrive at the fractional version of Dirac's equation which, whenever coupled to an external electromagnetic field and reduced to the nonrelativistic regime, yields a fractional Pauli-type equation. From the latter, we are able to present an explicit expression for the gyromagnetic ratio of charged fermions in terms of the fractionality parameter. We then focus our efforts to relate the coarse-grained property of space-time to fractionality and to the (g-2) anomalies of the different leptonic species.