Semiclassical analysis of Dirac fields on curved spacetime

Abstract

We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hslash$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat both massive and massless Dirac fields and show how a covariantly defined Berry connection and the associated Berry curvature govern the semiclassical dynamics. The gravitational spin Hall equations are shown to be particular cases of the Mathisson-Papapetrou equations for spinning objects.

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Cited by in corpus (18)

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• Probing general relativistic spin-orbit coupling with gravitational waves from hierarchical triple systems
• Spin Hall effects in the sky
• Weyl geometric effects on the propagation of light in gravitational fields
• TDiff invariant gauge fields in cosmology
• Gravitational wave memory and its effects on particles and fields
• Curved-spacetime dynamics of spin-$\frac{1}{2}$ particles in superposed states from a WKB approximation of the Dirac equation
• Conserved quantities and integrability for massless spinning particles in general relativity
• Gravity-induced birefringence in spherically symmetric spacetimes
• Neutrino spin oscillation in screening models revisited
• Quantum geometric tensors from sub-bundle geometry
• Pauli equation and charged spin-1/2 particle in a weak gravitational field
• The precession of particle spin in spherical symmetric spacetimes
• Deflection of Massive Spin-$\frac{1}{2}$ Particles around Kerr Black Hole
• Spin oscillations of neutrinos scattered by the supermassive black hole in the galactic center
• Quantum interferometry in external gravitational fields
• Dynamics of charged spin-$\frac{1}{2}$ particles in superposed states minimally coupled to electromagnetism in curved spacetime within the WKB approximation
• Dirac Equation with Space Contributions Embedded in a Quantum-Corrected Gravitational Field