We consider a 3-dimensional elastic continuum whose material points can experience only rotations and no displacements. Our dynamical variables are a coframe and a density; the metric is assumed to be prescribed (given). We choose a potential energy which is conformally invariant and combine it with kinetic energy to get the Lagrangian of our theory. We rewrite our field equations in terms of a spinor field and seek stationary (harmonically oscillating in time) solutions. We prove arXiv:0902.1268 that our field equations are equivalent to a pair of Weyl equations (massless Dirac equations).
Our model is similar to those in the theory of teleparallelism promoted by Einstein and Cartan, the difference being that a) we do not vary the metric and b) we choose a particular, conformally invariant Lagrangian overlooked by researchers in the subject area. The constraint of a prescribed metric can, of course, be eventually dropped and our hope is that variation of the metric would lead to a sensible description of the interaction of the particle with the gravitational field.