Field quantization and wave particle duality

Abstract

We owe to Pascual Jordan the first formulation of a theory of quantized fields, in the framework of Heisenberg’s matrix mechanics. For Jordan it is quantization which creates particles, both photons and electrons. The purpose of the present paper is to show that a coherent development of Jordan’s program leads to a formulation of quantum field theory in terms of ensemble averages of the field’s dynamical variables, in which no reference at all is made to the Schrödinger wave functions of “first quantization.” In this formulation the wave particle duality is no longer a puzzling phenomenon. The wave particle duality is instead, in this new perspective, only the manifestation of two complementary aspects (continuity vs. discontinuity) of an intrinsically nonlocal physical entity (the field) which objectively exists in ordinary three-dimensional space. This theory, in which the field’s statistical properties are represented by Wigner pseudoprobabilities deduced without any reference to Schrödinger wave functions, is based on two postulates. The first one is the requirement of invariance under canonical transformations of the probability distributions of a classical statistical description of the field’s state. This invariance leads to an uncertainty relation for the conjugated variables of the field’s oscillators. The second postulate is quantization. This means to assume that the intensity of each monochromatic wave should only have discrete values instead of the continuous range allowed by the classical theory. These two postulates can be satisfied only if the system’s physical variables are represented by noncommuting numbers. In this way what is generally assumed as a basic mathematical postulate in the standard formulation of quantum mechanics, follows from the physical postulates of the theory.