  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 10
independent components of the metric tensor and the 64 connection coefficients
are the unknowns of the theory. We write the Yang-Mills action for the affine
connection and vary it both with respect to the metric and the connection. 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 detailed
examination of this special subfamily suggests the possibility of using it to
model the neutrino. Our model naturally contains only two distinct types of
particles which may be identified with left-handed neutrinos and right-handed
antineutrinos.
