The Foldy-Wouthuysen transformation with Dirac matrices in the chiral representation: closed expressions for energy operators of fermions moving in electrostatic fields

In this paper, we obtain the closed expressions for energy operators in the Foldy-Wouthuysen representation in the presence of electrostatic fields. We also establish the connection between the Foldy-Wouthuysen representation and the Feynman-Gell-Mann representation.