  In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac
Hamiltonian and the self-adjoint Hamiltonian H_{\eta} with a flat scalar
product of the wave functions are physically equivalent. Operators of
transformation of Chandrasekhar's Hamiltonian and wave functions to the
\eta-representation with a flat scalar product are defined explicitly. If the
domain of the wave functions of Dirac's equation in the Kerr field is bounded
by two-dimensional surfaces of revolution around the z axis, Chandrasekhar's
Hamiltonian and the self-adjoint Hamiltonian in the \eta-representation are
Hermitian with equality of the scalar products,(\psi, H \varphi)=(H \psi,
\varphi).

General Relativity and Quantum Cosmology