Synopses & Reviews
It has been known since the 1930s that quantum mechanics can be formulated in quaternionic as well as complex Hilbert space. But systematic work on the quaternionic extension of standard quantum mechanics has scarcely begun. Authored by a world-renowned theoretical physicist, this book signals a major conceptual advance and gives a detailed development and exposition of quaternionic quantum mechanics for the purpose of determining whether quaternionic Hilbert space is the appropriate arena for the long sought-after unification of the standard model forces with gravitation. Significant results from earlier literature, together with many new results obtained by the author, are integrated to give a coherent picture of the subject. The book also provides an introduction to the problem of formulating quantum field theories in quaternionic Hilbert space. The book concludes with a chapter devoted to discussions on where quaternionic quantum mechanics may fit into the physics of unification, experimental and measurement theory issues, and the many open questions that still challenge the field. This well-written treatise is a very significant contribution to theoretical physics. It will be eagerly read by a wide range of physicists.
Review
"Lucid. . . .Independently of the physical correctness of quaternionic quantum mechanics, comparing the alternative theory with standard quantum mechanics leads to a much better and deeper understanding of the usual formalism. In this sense the book presents not only a valuable investment for the expert, but also can be recommended to everybody interested in quantum mechanics or field theory."--Mathematical Reviews
Synopsis
This monograph presents a new conceptualization of quantum mechanics, using quaternions instead of complex numbers. The author gives a systematic treatment of quaternionic quantum mechanics which parallels the standard textbook treatment of complex quantum mechanics.
Synopsis
This book signals a major conceptual advance in quaternionic quantum mechanics; significant results from earlier literature, together with many new ones obtained by the author, are integrated to give a coherent picture of the subject.
Description
Includes bibliographical references (p. 553-562) and index.
Table of Contents
PART I: INTRODUCTION AND GENERAL FORMALISM
1. Introduction
2. General Framework of Quaternionic Quantum Mechanics
3. Further General Results in Quaternionic Quantum Mechanics
PART II: NON-RELATIVISTIC QUATERNIONIC QUANTUM MECHANICS
4. One-Particle Quantum Mechanics--General Formalism
5. Stationary State Methods and Phase Methods
6. Scattering Theory and Bound States
7. Methods for Time-Development
8. Single Channel Time-Dependent Formal Scattering Theory
9. Multi-Particle and Multi-Channel Methods
10. Further Multi-Particle Topics
PART III: RELATIVISTIC QUATERNIONIC QUANTUM MECHANICS
11. Relativistic Single Particle Wave Equations Spin-0 and Spin-1/2
12. More on Relativistic Wave Equations: The Spin-1 Gauge Potential, Lagrangian Formulations, and the Poincare Group
13. Quaternionic Quantum Field Theory
14. Outlook
Appendix A: Proof of the Jacobi Identity for the Generalized Poisson Bracket
Appendix B: Derivation of Gaussian Integral Formulas