Non-Relativistic Approximation of the Dirac Equation for Slow Fermions   in Static Metric Spacetimes
  We analyse the non-relativistic approximation of the Dirac equation for slow fermions 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, induced by a static metric of spacetime. The derivation of the non-relativistic Hamilton operator of the Dirac equation is carried out by using a standard Foldy-Wouthuysen (SFW) transformation. We discuss the chameleon field as source of a torsion field and torsion-matter interactions. 
A. N. Ivanov, M. Pitschmann
gr-qc hep-ph nucl-ex