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Physics Bulletin

Mathematical Foundations of Quantum Theory

T. W. B. Kibble

Published May 1, 1979• 173 citations
Publisher

Abstract

A R Marlow (ed) 1978 New York: Academic x + 372 pp price £14.30 This book contains papers presented at a conference held in New Orleans in June 1977, at which physicists and mathematicians came together to discuss the foundations of quantum mechanics. Some of the very mathematical articles will be of interest only to specialists, but others clearly show a real effort to communicate across the disciplinary barrier.

DOI
10.1088/0031-9112/30/5/034

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A R Marlow (ed) 1978 New York: Academic x + 372 pp price £14.30 This book contains papers presented at a conference held in New Orleans in June 1977, at which physicists and mathematicians came together to discuss the foundations of quantum mechanics. Some of the very mathematical articles will be of interest only to specialists, but others clearly show a real effort to communicate across the disciplinary barrier.
Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface. The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.