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A brief treatment of spinors in general coordinates is given. The mathematical results are used to derive the Hamiltonian for a spinor field interacting with the gravitational field. The Hamiltonian formulation follows a method developed by Dirac, which has been used by Pirani and Schild to treat the free gravitational field. The Dirac method is further used here to carry out a reduction of the Hamiltonian to a form suitable for quantization. The quantization procedure is actually given, and the problems arising in connection with it---such as the factor ordering ambiguity and the vacuum expectation value of the spinor stress density---are discussed.
DeWitt et al. (Tue,) studied this question.