Gauge invariance in fractional field theories

TL;DR

This paper extends gauge invariance principles to fractional wave equations, deriving interaction terms and applying them to reproduce baryon spectra and explore fractional spin properties.

Contribution

It introduces gauge invariance in fractional field theories and applies it to fractional quantum equations, revealing fractional spin and reproducing baryon spectra.

Findings

Fractional Zeeman effect reproduces baryon spectrum accurately.

Internal fractional spin is deduced from fractional Schrödinger equation.

Gauge invariance principles are extended to fractional derivatives.

Abstract

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order $o(\bar{g})$ in the coupling constant $\bar{g}$. As a first application, based on the Riemann-Liouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately. The transformation properties of the non relativistic fractional Schr\"odinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.