University of Bahrain
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Massless Dirac equation as a special case of Cosserat elasticity

Show simple item record Chervova, Olga Vassiliev, Dmitri 2018-07-25T10:11:46Z 2018-07-25T10:11:46Z 2009
dc.identifier.issn 1815-3852
dc.description.abstract We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework is a special case of the so-called Cosserat theory of elasticity. Rotations of points of the continuum are described by attaching to each point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose a coframe and a density. We write down a potential energy which is conformally invariant and then incorporate time in the standard Newtonian way, by subtracting kinetic energy. Finally, we rewrite the resulting nonlinear variational problem in terms of an unknown spinor field. We look for quasi-stationary solutions, i.e. solutions that harmonically oscillate in time. We prove that in the quasi-stationary setting our model is equivalent to a pair of massless Dirac equations. The crucial element of the proof is the observation that our Lagrangian admits a factorization en_US
dc.language.iso en en_US
dc.publisher University of Bahrain en_US
dc.rights Attribution-NonCommercial-ShareAlike 4.0 International *
dc.rights.uri *
dc.title Massless Dirac equation as a special case of Cosserat elasticity en_US
dc.type Article en_US
dc.source.title Arab Journal of Basic and Applied Sciences
dc.abbreviatedsourcetitle AJBAS

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