Operators of quantum theory of Proca’s free field

Abstract The principal one-particle operators of quantum theory of Proca’s free field are derived using a method associating to any operator in a configuration representation a pair of operators acting directly on particle and antiparticle wave vectors in momentum representation, without affecting the mode vectors. This framework enables an effective quantization procedure giving a large set of one-particle operators with physical meaning as the spin and orbital angular momentum operators, the generators of Lorentz boosts, or the position and velocity operators. It is shown that the actions of all of these operators depend on polarization that can be defined in various ways because of the degrees of freedom of spin symmetry defined here for the first time. This determines the form of polarization vectors and connection coefficients that govern the form and action of all operators in momentum representation and ultimately of the one-particle operators of quantum theory. The role of connection coefficients is discussed, drawing the conclusion that it is less probable that they produce measurable physical effects.