Torsion waves in metric-affine field theory

The approach of metric-affine field theory is to define spacetime as a real oriented 4-manifold equipped with a metric and an affine connection. The 1 0 independent components of the metric tensor and the 64 connection coeffic ients are the unknowns of the theory. We write the Yang-Mills action for th e affine connection and vary it both with respect to the metric and the con nection. We find a family of spacetimes which are stationary points. These spacetimes are waves of torsion in Minkowski space. We then find a special subfamily of spacetimes with zero Ricci curvature; the latter condition is the Einstein equation describing the absence of sources of gravitation. A d etailed examination of this special subfamily suggests the possibility of u sing it to model the neutrino. Our model naturally contains only two distin ct types of particles which may be identified with left-handed neutrinos an d right-handed antineutrinos.