On the quantization of the Maxwell field with three polarization directions

Abstract

The unsatisfactory situation of the well-known quantization procedures of the Maxwell field (Coulomb gauge,Fock—Podolsky method,Gupta—Bleuler formalism [1]) has been stressed by many authors in the last years, and a considerable number of new proposals have been made [2]. Joining the idea ofNovobatzky andValatin [3], that the Maxwell field possesses only three polarization degrees of freedom, we present here a form of quantum electrodynamics with full use of the Lorentz condition. The resulting commutation relations correspond with those ofValatin; the Hilbert space, as far as it has been investigated, proves to be of definite metric. Some results have already been published [4].