  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 factorisation.
