Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime

We present the manifestly covariant Lagrangian of a massless polarized particle, that implies all dynamic and algebraic equations as the conditions of extreme of this variational problem. The model allows for minimal interaction with a gravitational field, leading to the equations, coinciding with Maxwell equations in the geometrical optics approximation. The model allows also a wide class of non minimal interactions, which suggests an alternative way to study the electromagnetic radiation beyond the leading order of geometrical optics. As a specific example, we construct a curvature-dependent interaction in Schwarzschild spacetime, predicting the Faraday rotation of polarization plane, linearly dependent on the wave frequency. As a result, the Schwarzschild spacetime generates a kind of angular rainbow of light: waves of different frequencies, initially linearly-polarized in one direction, acquire different orientations of their polarization planes when propagate along the same ray.