Quaternionic Quantum Mechanics and Quantum Fields by Stephen L. Adler

Quaternionic Quantum Mechanics and Quantum Fields

byStephen L. Adler

Hardcover | April 27, 1995

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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 booksignals 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 concludeswith 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 theoreticalphysics. It will be eagerly read by a wide range of physicists.

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Title:Quaternionic Quantum Mechanics and Quantum FieldsFormat:HardcoverDimensions:608 pages, 9.49 × 6.5 × 1.5 inPublished:April 27, 1995Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:019506643X

ISBN - 13:9780195066432

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Table of Contents

PART I: INTRODUCTION AND GENERAL FORMALISM1. Introduction2. General Framework of Quaternionic Quantum Mechanics3. Further General Results in Quaternionic Quantum MechanicsPART II: NON-RELATIVISTIC QUATERNIONIC QUANTUM MECHANICS4. One-Particle Quantum Mechanics--General Formalism5. Stationary State Methods and Phase Methods6. Scattering Theory and Bound States7. Methods for Time-Development8. Single Channel Time-Dependent Formal Scattering Theory9. Multi-Particle and Multi-Channel Methods10. Further Multi-Particle TopicsPART III: RELATIVISTIC QUATERNIONIC QUANTUM MECHANICS11. Relativistic Single Particle Wave Equations Spin-0 and Spin-1/212. More on Relativistic Wave Equations: The Spin-1 Gauge Potential, Lagrangian Formulations, and the Poincare Group13. Quaternionic Quantum Field Theory14. OutlookAppendix A: Proof of the Jacobi Identity for the Generalized Poisson BracketAppendix B: Derivation of Gaussian Integral Formulas

Editorial Reviews

"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 forthe expert, but also can be recommended to everybody interested in quantum mechanics or field theory."--Mathematical Reviews