# Modelling the neutrino in terms of Cosserat elasticity - Mathematical Physics

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Abstract: The paper deals with the Weyl equation which is the massless Dirac equation.We study the Weyl equation in the stationary setting, i.e. when the the spinorfield oscillates harmonically in time. We suggest a new geometricinterpretation of the stationary Weyl equation, one which does not require theuse of spinors, Pauli matrices or covariant differentiation. We think of our3-dimensional space as an elastic continuum and assume that material points ofthis continuum can experience no displacements, only rotations. This frameworkis a special case of the Cosserat theory of elasticity. Rotations of materialpoints of the space continuum are described mathematically by attaching to eachgeometric point an orthonormal basis which gives a field of orthonormal basescalled the coframe. As the dynamical variables unknowns of our theory wechoose the coframe and a density. We choose a particular potential energy whichis conformally invariant and then incorporate time into our action in thestandard Newtonian way, by subtracting kinetic energy. The main result of ourpaper is the theorem stating that in the stationary setting our model isequivalent to a pair of Weyl equations. The crucial element of the proof is theobservation that our Lagrangian admits a factorisation.

Author: ** Olga Chervova, Dmitri Vassiliev**

Source: https://arxiv.org/