Comment on "Spin in an arbitrary gravitational field" arXiv:1308.4552

Abstract: The authors of that work [Phys. Rev. D 88, 084014 (2013)], arXiv:1308.4552, derive quantum-mechanical equations valid for the covariant Dirac equation by restricting the choice of the tetrad field through the use of the "Schwinger gauge". Yet it has been shown previously that this gauge leaves space for a physical ambiguity of the Hamiltonian operator. It is shown here precisely how this ambiguity occurs with their settings. There is another ambiguity in the Foldy-Wouthuysen Hamiltonian, for the time-dependent case which is relevant here. However, their equations of motion for classical spinning particles are unambiguous.