Equivalence and Hermiticity of Dirac Hamiltonians in the Kerr gravitational field

Abstract

In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac Hamiltonian and the self-adjoint Hamiltonian H_η with a flat scalar product of the wave functions are physically equivalent. Operators of transformation of Chandrasekhar's Hamiltonian and wave functions to the η-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 η-representation are Hermitian with equality of the scalar products,(ψ, H φ)=(H ψ, φ).

16 pages, accepted for publication in Annalen der Physik

References in corpus (3)

• Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems
• Uniqueness and Self-Conjugacy of Dirac Hamiltonians in arbitrary Gravitational Fields
• Solution of the problem of uniqueness and hermiticity of hamiltonians for Dirac particles in gravitational fields

Cited by in corpus (4)

• Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations
• Geometric phase in Taub-NUT spacetime
• Stationary solutions of the second-order equation for fermions in Kerr-Newman space-time
• Geometric phase for Dirac Hamiltonian under gravitational fields in the non-relativistic regime