Spin in an arbitrary gravitational field

Abstract

We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this framework, we find the Hermitian Dirac Hamiltonian for an arbitrary classical external field (including the gravitational and electromagnetic ones). In order to discuss the physical content of the quantum-mechanical model, we further apply the Foldy-Wouthuysen transformation, and derive the quantum equations of motion for the spin and position operators. We analyse the semiclassical limit of these equations and compare the results with the dynamics of a classical particle with spin in the framework of the standard Mathisson-Papapetrou theory and in the classical canonical theory. The comparison of the quantum mechanical and classical equations of motion of a spinning particle in an arbitrary gravitational field shows their complete agreement.

26 pages, no figures, Revtex

References in corpus (13)

• Spin dynamics in gravitational fields of rotating bodies and the equivalence principle
• Equivalence principle and experimental tests of gravitational spin effects
• Dynamics of Extended Spinning Masses in a Gravitational Field
• Canonical Formulation of Spin in General Relativity
• Dirac fermions in strong gravitational fields
• General Relativistic Effects of Gravity in Quantum Mechanics -- A Case of Ultra-Relativistic, Spin 1/2 Particles --
• 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
• Dynamics of test bodies with spin in de Sitter spacetime
• Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field
• Dirac equations in curved space-time versus Papapetrou spinning particles
• Spin Precession in Inertial and Gravitational Fields
• Classical and Quantum Spins in Curved Spacetimes

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