On the Quantization of Scalar and Spinor Fields in the Schwarzschild Space-Time

It is shown that a consistent procedure of canonical quantization of real scalar and spinor fields can be carried out without taking into account the interior of the Schwarzschild black hole, so that in the resulting theories the canonical (anti)commutation relations are satisfied exactly, and the Hamiltonians have the standard form. The spectra of states with energies both greater and smaller than the field mass turn out to be continuous. An interesting property of the resulting theories has been revealed: a doubling of the number of quantum states with energies greater than the field mass, which is a consequence of the topological structure of the Schwarzschild space-time.