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.