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We discuss the problem of canonical quantization of a free massive spinorfield in the Schwarzschild spacetime. It is shown that a consistent procedureof canonical quantization of the field can be carried out without taking intoaccount the internal region of the black hole, the canonical commutationrelations in the resulting theory hold exactly and the Hamiltonian has thestandard form. Spin sums are obtained for solutions of the Dirac equation inthe Schwarzschild spacetime.

Quantization of spinor field in the Schwarzschild spacetime and spin sums for solutions of the Dirac equation