Description

Book Synopsis
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.

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

Spinors in Hilbert Space 114 Cambridge Tracts in Mathematics Series Number 114

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    A Hardback by Roger Plymen, Paul Robinson

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      View other formats and editions of Spinors in Hilbert Space 114 Cambridge Tracts in Mathematics Series Number 114 by Roger Plymen

      Publisher: Cambridge University Press
      Publication Date: 12/1/1994 12:00:00 AM
      ISBN13: 9780521450225, 978-0521450225
      ISBN10: 0521450225

      Description

      Book Synopsis
      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.

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

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