Gauge invariance in fractional field theories

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order o(g¯) in the coupling constant g¯. 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 Schrödinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.