2014/06/10 by A. N. Ivanov, Mario Pitschmann, M. Pitschmann
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Dirac equation #Dirac fermion #Dirac sea #Fermion #Gravitation #Gravitational field #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime #gr-qc #hep-ph #nucl-ex
paper · pdf · doi:10.1103/physrevd.90.045040
8 pages
arxiv created 2014/06/10 · openalex publication_date 2014/08/28 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the nonrelativistic approximation of the Dirac equation for slow fermions, having small kinetic energies compared to their rest energy m and moving in spacetimes with a static metric, caused by the weak gravitational field of the Earth and a chameleon field, and derive the most general effective gravitational potential to order 1/m, induced by a static metric of spacetime excluding possible rotations of the coordinate frame. The derivation of the nonrelativistic Hamilton operator of the Dirac equation is carried out by using a standard Foldy--Wouthuysen transformation. We discuss the chameleon field as source of a torsion field and torsion--matter interactions.