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The exact exponential Foldy-Wouthuysen transformation operator applicable fora particle with an arbitrary spin is derived. It can be successfully utilizedfor verifying any Foldy-Wouthuysen transformation method based on theexponential operator. When a verified method is relativistic, the relativisticexponential operator should be expanded in the semirelativistic power series.The use of the obtained exponential operator for a derivation of theFoldy-Wouthuysen Hamiltonian makes it possible to check the validity of anyother method of the Foldy-Wouthuysen transformation, while this possibility mayneed a greater computational effort.

Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle