Journal of Physical Studies 5(1), 7–13 (2001) DOI: https://doi.org/10.30970/jps.05.7 ON THE COMPARISON OF SOLUTIONS OF THE DIRAC AND MATHISSON–PAPAPETROU EQUATIONS IN A SCHWARZSCHILD FIELD R. Plyatsko Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine, 3-b Naukova Str., Lviv, UA-79601, Ukraine} \addressu{ Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України вул. Наукова, 3-б, Львів, 79601, Україна

The importance of the analysis of the Dirac equation solutions corresponding to such ultrarelativistic solutions of the Mathisson-Papapetrou equations which are caused by the essential influence of the gravitational spin-orbit interaction is discussed. As the first step in this direction we consider the partial solution of the Dirac equation in a Schwarzschild field corresponding to the solution of the Mathisson-Papapetrou equations describing the circular ultrarelativistic orbit of radius $r=3M$, where $M$ is a Schwarzschild mass.

PACS number(s): 04.20.Cv, 11.10.Qr, 95.30.Sf

ps pdf