  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 spinor
field oscillates harmonically in time. We suggest a new geometric
interpretation of the stationary Weyl equation, one which does not require the
use of spinors, Pauli matrices or covariant differentiation. We think of our
3-dimensional space as an elastic continuum and assume that material points of
this continuum can experience no displacements, only rotations. This framework
is a special case of the Cosserat theory of elasticity. Rotations of material
points of the space continuum are described mathematically by attaching to each
geometric point an orthonormal basis which gives a field of orthonormal bases
called the coframe. As the dynamical variables (unknowns) of our theory we
choose the coframe and a density. We choose a particular potential energy which
is conformally invariant and then incorporate time into our action in the
standard Newtonian way, by subtracting kinetic energy. The main result of our
paper is the theorem stating that in the stationary setting our model is
equivalent to a pair of Weyl equations. The crucial element of the proof is the
observation that our Lagrangian admits a factorization.
