Quaternionic Quantum Mechanics and Quantum Fields

by Adler, Stephen L.

• ISBN13: 9780195066432
• ISBN10: 019506643X
• Format: Hardcover
• Copyright: 1995-04-27
• Publisher: Oxford University Press

Summary

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.

Table of Contents

Introduction And General Formalism

Introduction

General Framework of Quaternionic Quantum Mechanics

Further General Results in Quaternionic Quantum Mechanics

Non-Relativistic Quaternionic Quantum Mechanics

One-Particle Quantum Mechanics--General Formalism

Stationary State Methods and Phase Methods

Scattering Theory and Bound States

Methods for Time-Development

Single Channel Time-Dependent Formal Scattering Theory

Multi-Particle and Multi-Channel Methods

Further Multi-Particle Topics

Relativistic Quaternionic Quantum Mechanics

Relativistic Single Particle Wave Equations Spin-0 and Spin-1/2

More on Relativistic Wave Equations: The Spin-1 Gauge Potential, Lagrangian Formulations, and the Poincare Group

Quaternionic Quantum Field Theory

Outlook

Proof of the Jacobi Identity for the Generalized Poisson Bracket

Derivation of Gaussian Integral Formulas

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