Decompositions in Quantum Mechanics—An Overview

Abstract

AbstractThere is current interest in using ideas from quantum mechanics in the study of economics. We give an overview of an approach to quantum mechanics rooted not necessarily in Hilbert space, but in the primitive mathematical idea of direct products. This approach includes the standard von Neumann Hilbert space approach. It provides a conceptually simpler understanding of issues from standard quantum mechanics, and offers possibilities beyond the standard Hilbert space formulation. These further possibilities may be of particular interest in consideration of economics where the aim is to exploit quantum principles rather than specific physical situations.