2000/10/18 by P. Alsing, P. M. Alsing, James Evans +2 · 51 citations
Physics and Astronomy · #Classical mechanics #Gravitational field #Neutrino Physics Research #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spin (aerodynamics) #WKB approximation #Wave equation #Wave function #gr-qc
paper · pdf · doi:10.1023/a:1012284625541
published in General Relativity and Gravitation 33(9), 1459-1487 (Springer Science+Business Media) · 30 pages, no figures. Submitted to Gen.Rel.Grav 17 Oct 00
arxiv created 2000/10/18 · openalex publication_date 2001/09/01 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is S/ℏ = ∫ pμ dxμ / ℏ, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple managable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has exactly the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in ℏ. We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in ℏ. For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.