In this paper we offer an expression of the general Foldy-Wouthuysen transformation in the chiral representation of Dirac matrices interacting with fermion field. Our hypothesis is that through the multiplication of the Pauli matrix and Maxwell's chiral equations in the case of <img border=0 width=51 height=25 src="/fbpe/img/ingeniare/v16nespecial/image07-1.gif">,one obtains the Dirac's chiral equation. This is the proof of the theorem that the wave mechanics of quantum particles represent a specialized electrodynamic.