Derivation of Equal-Time Commutation Relations in a Self-Consistent Quantum Field Theory

Abstract

A self-consistent quantum field theory is proposed wherein the field equations for the Heisenberg fields are postulated. The Heisenberg fields are required to be linear combinations of normal products of the physical free fields, and the coefficients of the expansion are determined self-consistently. No a priori knowledge of the equal-time commutation relations among the Heisenberg fields is assumed. Using a solvable model, it is shown that local microscopic causality requires the existence of a bound state.