Quaternionic Quantum Mechanics and Quantum Fields (International Series of Monographs on Physics) 1st Edition by Stephen L. Adler | (PDF) Free Download

Description

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 ofunification, 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.

User’s Reviews

Editorial Reviews: 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 About the Author Stephen L. Adler is at Institute for Advanced Study.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Birkhoff and Von Neumann (1936) posited that a quaternionic quantum mechanics, i.e., a quantum mechanics where wave functions or probability amplitudes are quaternion valued rather than the usual complex valued, was in principle possible though they never followed through with this program. Dr. Adler follows the program through in this text. He develops the formalism and shows that it satisfies the Hilbert space formulation (quantum mechanical postulates) and goes on to develop the typical corresponding ingredients you’d see in a quantum mechanics course in this formalism, e.g., angular momentum and the ladder operators. In a naive sense an extension like this might bear fruit as the quaternion units or bases satisfy the Pauli spin algebra and in fact the spin matrices may be substituted (a factor of the imaginary i is needed) for these units with no change in structure. So some advantage can be expected in handling spin-a not so trivial feature of the usual quantum mechanics. Other systems which obey a Clifford algebra are also explored like octonions which are showed not to support a Hilbert space formulation . This text was written at a time when hope for string theory was waning-Non-uniqueness of vacuum! Some hoped that maybe a modification and extension of quantum mechanics which did not spoil its proven successful features might bring useful tools to this problem. It still may-the author believes if there are energies beyond the Planck scale, i.e, beyond superstrings this type of quantum mechanics could produce a useful modification. A good text to introduce you to the power of quaternions and quaternionic analysis is A.J.Hanson’s “Visualizing Quaternions.”

⭐This book is a good example of what can be done with the quaternionic formalism to improve some treatments of theoretical physics. However, it is not more than a formal improvement, of course taking advantadge of the arithmetical properties of quaternions and their ability to represent space rotations and other transformations needed in physics, for the author misses the opportunity of using the full power of quaternions by ignoring completely quaternionic ANALYSIS. He even says that this kind of analysis is not useful for physics. He obvioulsly has not read enough on the subject.The book is useful to learn how to REPRESENT problems by means of quaternions, but to SOLVE them you need the analysis, a feature this book lacks.Contents: Introduction; General Framework of Quaternionic Quantum Mechanics; Further General Results in 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; Multiparticle and Multichannel Methods; Further Multiparticle Topics; 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 Poincaré Group; Quaternionic Quantum Field Theory; Outlook; 2 Appendices.Motivates each topic though a previous knowledge of quantum mechanics is required. Extensive list of references. Nice printing quality and clothbound.

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