Spinors in Hilbert Space

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

The concept of spinors originated in the quantum mechanical study of electrons. The authors give a definitive self-contained account of the subject, with complete proofs, many of which offer a fresh perspective. It will appeal to a wide audience in mathematics and mathematical physics.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.