On Sectorial Photon Theories Reconstructing Einstein’s Early Fusion Picture for Light

Abstract

This is the second part of a pair of companion papers devoted to an analysis of Einstein’s fusion picture for light. While in the foregoing paper “An Actual Discusion of Einstein’s Early Fusion Picture for Photons and Classical Maxwell Fields” (referred to as Rieckers 2025) our conclusions ended with the historical ab initio motivation and mathematical elaboration of a multi-photon theory in Fock space, we now start from the non–separable C*-Weyl algebra gained by abstracting the Fock–represented Weyl algebra. To the rich state space of this antiliminary observable algebra we apply notions of a convex state space approach to identify sub–theories that cover classical field states (including the vacuum with classical zero–field), that are possibly decorated by photonic quantum noise. The main emphasis is laid on direct integrals over irreducible, disjoint representations of the C*-Weyl algebra, decomposing the effective photon theory into sectors. Certain limits of smeared central field operators suggest a mathematical realization of Einstein’s early photon notion consisting of an energy point surrounded by a local force field (respective wave function). Macroscopic classical Maxwell fields are gained by superposing the expectation values of products of those composite photon operators. The ontological status of the explicated photon notion is discussed. Connections to Einstein’s historic photon theory, summarized in Rieckers (2025), as well as to quantum optical applications are hinted at throughout the paper.