Spin-orbit couplings of quantum fields in Schwarzschild spacetime

In Schwarzschild spacetime, the gravitational spin-orbit couplings of the massless Dirac field and the photon field can be studied in a unified way. In contrary to the previous investigations presented mainly at the quantum-mechanical level, our work is presented at the level of quantum field theory without resorting to the Foldy-Wouthuysen transformation. If massless Dirac particles and photons have the same momentums, their energy-level splittings due to the gravitational spin-orbit couplings are the same. Massless Dirac particles and photons coming from the Hawking radiations are partially polarized as long as their original momentums are not parallel to the radial direction of a Schwarzschild black hole.