Unitary transformation for new diagonalization of Dirac Hamiltonian

The Foldy–Wouthuysen transformation was originally developed to elucidate the nonrelativistic limit of the Dirac equation. In this paper, we introduce a novel unitary transformation for the Hamiltonian of the Dirac equation. The unitary transformation operator is given by [Formula: see text] which results in the diagonal Hamiltonians [Formula: see text] and [Formula: see text]. We also apply this new unitary transformation to wave function calculations, and elaborate on its significance.