Non-Relativistic Approximation of Dirac Equation for Slow Fermions Coupled to the Chameleon and Torsion Fields in the Gravitational Field of the Earth

摘要

We analyse a non-relativistic approximation of the Dirac equation for slowfermions, coupled to the chameleon field and torsion in the spacetime with theSchwarzschild metric, taken in the weak gravitational field of the Earthapproximation. We follow the analysis of the Dirac equation in the curvedspacetime with torsion, proposed by Kostelecky (Phys. Rev. D69, 105009 (2004)),and apply the Foldy--Wouthuysen transformations. We derive the effectivelow-energy gravitational potentials for slow fermions, coupled to thegravitational field of the Earth, the chameleon field and to torsion withminimal and non-minimal couplings.