2013/06/22 by J. Weberszpil, J. A. Helayël-Neto, J. Abdalla Helayël-Neto
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Coupling (piping) #Electromagnetic field #Expression (computer science) #Fermion #Field (mathematics) #Focus (optics) #Helicity #Lepton #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1155/2014/572180
published as Advances in High Energy Physics Volume 2014 (2014), Article ID 572180 · 15 pages
arxiv created 2013/06/22 · openalex publication_date 2014/01/01 · arxiv updated 2014/07/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>g</mml:mi><mml:mo>-</mml:mo><mml:mn fontstyle="italic">2</mml:mn></mml:math>) anomalies of the different leptonic species.