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.

• Received 29 February 1952

DOI:https://doi.org/10.1103/PhysRev.87.116