General Relativistic Equations Of Motion Research Articles

Representations of Dirac equation in general relativity

After a reformulation of the General Relativistic equations of motion of a point mass in a gravitational field in terms of « fourlegs », the generalized Dirac equation is written in the Schrodinger representation and the equations of motion of classical observable quantities compared with the previous one. The Foldy-Wouthuysen representation is obtained in presence of gravitational fields. The most interesting result is that the gravitational « gyromagnetic » factor is 1 instead of 2 as the electromagnetic one. The interpretation of this fact is that the spinor field (and probably all fields) describes rotating particles where the gravitational mass has exactly the same space distribution as the inertialo mass. This is not true in Moshinsky-Birkhoff linear theory. Finally the red shift of hydrogen atoms levels in presence of gravitational field is obtained and found to coincide with the usual prediction of General Relativity.