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Ludwig G. An Axiomatic Basis for Quantum Mechanics. Volume 1: Derivation of Hilbert Space Structure

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Ludwig G. An Axiomatic Basis for Quantum Mechanics. Volume 1: Derivation of Hilbert Space Structure
Springer, 1985. - 243 pp.
This book is the first volume of a two-volume work, which is an improved version of a preprint published in German. The author seeks to deduce the fundamental concepts of quantum mechanics solely from a description of macroscopic devices. The microscopic systems such as electrons, atoms, etc. must be detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis of fossils. In this first volume a general description of macroscopic systems by trajectories in state spaces is developed. This general description is a basis for the special description of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and molecules, for instance the "elementary particles". The book not only gives an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.
Contents:
The Problem of Formulating an Axiomatics for Quantum Mechanics.
Pretheories for Quantum Mechanics.
Base Sets and Fundamental Structure Terms for a Theory of Microsystems.
Embedding of Ensembles and Effect Sets in Topological Vector Spaces.
Observables and Preparators.
Main Laws of Preparation and Registration.
Decision Observables and the Center.
Representation of ℬ, ℬ’ by Banach Spaces of Operators in a Hilbert Space.
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