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Spinors, Clifford, and Cayley Algebras (Interdisciplinary Mathematics Series Vol 7): Robert Hermann

Ths material in this Volume is mostly a continuation of Volumes I and II. I have found that what used to be called "abstract algebra" - in the older van der Waerden, Birkhoff and McLane tradition - is very useful in many applied areas. I have already presented scattered applications to Systems Theory in Volume III, and more systematically in Volume VIII. This Volume develops material which is closely linked with Physics.

Most of this Volume is "well-known," in the sense that it is ospsible to dig it out of the standard literature in algebra. The novelty lies in an attempt to present it at an intermediate level of abstractness, and to concentrate on the material that I have found of most use in Physics. In fact, there are further applications one can make, particularly to elementary particle theory and quantum mechanics, and the last chapter briefly touches on such connections. The material is also very useful in Lie and finite group theory, and I certainly plan more work in this direction.

As to Prerequisites and Background, Volumes I and II should be adequate. Knowledge of some standard material on group theory, from the physicists' point of view, should be useful. The book by Miller [1], and my own "Lectures in Mathematical Physics, vol. II" should serve.

Again, I use abbreviations (e.g. DGCV, LGP) to refer to my own books. Prof. John Stachel has provided excellent scientific hospitality, inspiration and working conditions for me as a visitor at the Institute for Relativity Studies of Boston University. I again thank Mrs. Alta Zapf for her fine typing.

CONTENTS: (CHAPTER TITLE/page number/CHAPTER KEYWORDS)

Preface 1 associative algebra, linear maps, vector space

Chapter II 53 division algebra, associative algebra, vector space

Chapter III 111 Clifford algebra, tensor algebra, Dirac matrices

Chapter IV 141 Clifford algebra, Lorentz group, orthogonal group

Chapter V 185 composition algebra, Cayley algebra, absolute parallelism

Chapter VI 243 differential operator, Maxwell equations, Lorentz group

Bibliography 275

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