On the determination of the field operator representation in canonical model quantum field theory

Abstract

In a canonical quantum field theory,i.e. based on the canonical commutation relations, the choice of an adequate field operator representation compatible with an assumed model of interaction is quite difficult to construct, unless the so-called vacuum expectation functional of the fieldE(f,g) = 〈Ω|U†(f,g)|Ω〉 is known. Here |Ω〉 is the vacuum state of the representation,U(f, g) is the Weyl operator of a neutral scalar field. In this paper a determination ofE(f, g) in a quartic self-interaction model is proposed as the invariant, positive and normalized function under the action of a system of partial differential functional operators, which form a representation of the Poincare-group generators.