State Representations for Renormalized Energy Equations in Quantum Field Theory

Quantum fields with interaction do not allow the application of the Fock representation. Rather the algebraic G.N.S. procedure has to be used which leads to nonorthonormal basis states. This raises the problem of explicit state construction with respect to such states. In the present paper this problem is treated for the case of a sufficiently regularized, selfinteracting spinorfield. By some theorems it is demonstrated that a consequent treatment of its field Hamiltonian which respects the general algebraic requirements leads to Dyson's renormalized energy equation. In addition this approach allows explicit state constructions which so far have not been realized in conventional quantum field theory.