Gauge invariance in fractional field theories

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 Schrödinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.

arXiv commentremarks on fractional spin added, references added, in press Phys.Lett.A

References in corpus (5)

• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• The Cosmological Parameters 2006
• Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives
• Relativistic wave equations with fractional derivatives and pseudo-differential operators
• The fractional symmetric rigid rotor

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• Common aspects of q-deformed Lie algebras and fractional calculus
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• The DuBois-Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler-Lagrange Equation Involving only Derivatives of Caputo
• Fractional dynamic symmetries and the ground state properties of nuclei
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• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
• The Lagrangian for mass dimension one fermionic dark matter
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• Propagation dynamics of abruptly autofocusing circular Airy-Gaussian vortex beams in the fractional Schrödinger equation
• Electron Spin Precession for the Time Fractional Pauli Equation
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