Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-06-08
Phys.Rev. D74 (2006) 065017
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12pt LaTeX, 17 pages. v2: version accepted for publication in Phys.Rev.D: comments on scalar product changed, using a recent p
Scientific paper
10.1103/PhysRevD.74.065017
We study first the Hamiltonian operator H corresponding to the Fock-Weyl extension of the Dirac equation to gravitation. When searching for stationary solutions to this equation, in a static metric, we show that just one invariant Hermitian product appears natural. In the case of a space-isotropic metric, H is Hermitian for that product. Then we investigate the asymptotic post-Newtonian approximation of the stationary Schroedinger equation associated with H, for a slow particle in a weak-field static metric. We rewrite the expanded equations as one equation for a two-component spinor field. This equation contains just the non-relativistic Schroedinger equation in the gravity potential, plus correction terms. Those "correction" terms are of the same order in the small parameter as the "main" terms, but are numerically negligible in the case of ultra-cold neutrons in the Earth's gravity.
No associations
LandOfFree
Post-Newtonian equation for the energy levels of a Dirac particle in a static metric does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Post-Newtonian equation for the energy levels of a Dirac particle in a static metric, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Post-Newtonian equation for the energy levels of a Dirac particle in a static metric will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-506882