Spinors in Hilbert Space

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.