Foldy-Wouthuysen transformation for equations connected to the de Sitter group

Foldy–Wouthuysen transformation for the equations connected with the De Sitter group $SO(1,4)$ is considered. The general transformation contains the usual Foldy–Wouthuysen transformation and the Cini–Touschek transformation. It is shown that the usual Foldy–Wouthuysen transformation is equivalent to the Lorentz transformation only for the edge weight points with $h=\pm\, n_1$ of the De Sitter group representation ($n_1,n_2$). An equation in the Cini–Touschek representation is for $h=\pm\, n_1$ equivalent to equations for the zero rest mass particles. From the known equations connection between the Foldy–Wouthuysen and Lorentz transformations exists for the Dirac, Kemmer–Duffin and Bargmann–Wigner equations. For the Rarita–Schwinger equation in the $SO(1,4)$-form there is no equivalence.