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

TL;DR

This paper develops a consistent method for quantizing a free massive spinor field in Schwarzschild spacetime, deriving spin sums and ensuring standard canonical relations without involving the black hole's interior.

Contribution

It presents a novel approach to canonical quantization of spinor fields in Schwarzschild spacetime, including explicit spin sums and a clear treatment of the external region.

Findings

Canonical quantization is feasible without the black hole interior.

Canonical commutation relations are preserved exactly.

Standard form of the Hamiltonian is obtained.

Abstract

We discuss the problem of canonical quantization of a free massive spinor field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the internal region of the black hole, the canonical commutation relations in the resulting theory hold exactly and the Hamiltonian has the standard form. Spin sums are obtained for solutions of the Dirac equation in the Schwarzschild spacetime.