Revisiting Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach With Axiomatic Local Metric Derivatives

Abstract

This contribution sets out to extend the concept of helicity so as to include it in a fractional scenario with a low-level of fractionality. To accomplish this goal, the authors write down the left- and the right-handed Weyl equations from first principles in this extended framework. Next, by coupling the two different fractional Weyl sectors by means of a mass parameter, they arrive at the fractional version of Dirac's equation, which, whenever coupled to an external electromagnetic field and reduced to the non-relativistic regime, yields a fractional Pauli-type equation. From the latter, they are able to present an explicit expression for the gyromagnetic ratio of charged fermions in terms of the fractionality parameter. They then focus their efforts to relate the coarse-grained property of space-time to fractionality and to the (g-2) anomalies of the different leptonic species. To do this, they build up an axiomatic local metric derivative that exhibits the Mittag-Leffler function as eigenfunction and is valid for low-level fractionality, whenever the order parameter is close to 1.