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Published in:
2009 | OriginalPaper | Chapter
Dirac Equation as a Special Case of Cosserat Elasticity
Authors : James Burnett, Olga Chervova, Dmitri Vassiliev
Published in: Analysis, Partial Differential Equations and Applications
Publisher: Birkhäuser Basel
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We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by means of a Kaluza-Klein extension. Our Lagrangian density is proportional to axial torsion squared. The advantage of our approach is that it does not require the use of spinors, Pauli matrices or covariant differentiation. The only geometric concepts we use are those of a metric, differential form, wedge product and exterior derivative. We prove that in the special case with no dependence on the third spatial coordinate our model is equivalent to the Dirac equation. The crucial element of the proof is the observation that our Lagrangian admits a factorisation.