In physics literature, Dirac’s equation is usually introduced and studied on flat Minkowski spacetime [IZ80, Ka61], while spinors have been extensively used within the context of classical General Relativity. Generalization of the quantum theory to curved spacetime is not so popular, perhaps because formulation of QFT on a curved background encounters severe difficulties and even paradoxes. On the other hand, there exists a rich mathematical literature about spinor structures and the Dirac equation on curved spacetime and general Riemannian manifolds, based essentially on the language of groups and principal bundles.