Spinors in Hilbert Space

A definitive self-contained account of the subject. Of appeal to a wide audience in mathematics and physics.

Roger Plymen (Author), Paul Robinson (Author)

9780521450225, Cambridge University Press

Hardback, published 1 December 1994

180 pages
23.6 x 15.8 x 1.6 cm, 0.394 kg

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject. The book will therefore appeal to a wide audience of graduate students and researchers in mathematics and mathematical physics.

Introduction
1. Clifford algebras
2. Fock representations
3. Implementation and equivalence
4. Spin groups
Appendix
Bibliography
Index.

Subject Areas: Calculus & mathematical analysis [PBK]