Quantenlogische Systeme und Tensorproduktraeume

TL;DR

This paper provides an intuitive construction of quantum logical systems and discusses how composed physical systems in quantum mechanics are represented by tensor product spaces, based on lattice and c-morphism theory.

Contribution

It offers a detailed logical and mathematical proof that quantum systems must be described using tensor product spaces, extending prior results with an intuitive approach.

Findings

Quantum systems are represented by tensor product spaces.

Logical axiomatic systems can describe composed quantum systems.

Mathematical proof confirms tensor product necessity in quantum mechanics.

Abstract

In this work we present an intuitive construction of the quantum logical axiomatic system provided by George Mackey. The goal of this work is a detailed discussion of the results from the paper 'Physical justification for using the tensor product to describe two quantum systems as one joint system' [1] published by Diederik Aerts and Ingrid Daubechies. This means that we want to show how certain composed physical systems from classical and quantum mechanics should be described logically. To reach this goal, we will, like in [1], discuss a special class of axiomatically defined composed physical systems. With the help of certain results from lattice and c-morphism theory (see [2] and [23]), we will present a detailed proof of the statement, that in the quantum mechanical case, a composed physical system must be described via a tensor product space.