Explicit Formal Construction of Nonlinear Quantum Fields

Abstract

It is shown that there can be associated with any given nonlinear relativistic partial differential equation an operator field satisfying the canonical commutation relations, transforming appropriately under the action of the Lorentz group, and propagated in accordance with the given differential equation. This quantization procedure is unique, apart from the scale of the commutators. The treatment is intuitive, but is capable of rigorization in terms of the mathematical theory of analysis in function space (functional integration). The results are in harmony with crucial conventional ones, so far as has been determined, and provide in principle a possible means of computing the collision matrix for particular systems without recourse to perturbation theory.