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Spinors in Hilbert Space (Cambridge Tracts in Mathematics) 1st Edition

5 out of 5 stars 1 customer review
ISBN-13: 978-0521450225
ISBN-10: 0521450225
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Editorial Reviews

Book Description

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.

From the Back Cover

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum physics of the free fermion field. This Tract begins with a definitive account of various Clifford algebras over a real Hilbert space. Chapter 2 contains a detailed account of creators, annihilators, Fock representations and parity. Transformation properties of Fock representation under Bogoliubov automorphisms are discussed in chapter 3: this leads to the restricted orthogonal group. In the final chapter the authors discuss inner Bogoliubov automorphisms and 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.
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Product Details

  • Series: Cambridge Tracts in Mathematics (Book 114)
  • Hardcover: 180 pages
  • Publisher: Cambridge University Press; 1 edition (January 27, 1995)
  • Language: English
  • ISBN-10: 0521450225
  • ISBN-13: 978-0521450225
  • Product Dimensions: 6 x 0.6 x 9 inches
  • Shipping Weight: 14.1 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #3,116,923 in Books (See Top 100 in Books)

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The authors present an exceptionally clear treatment of Clifford algebras, Clifford C*-algebras, and von Neumann Clifford algebras, their Fock representations and related developments. The proofs are concise and to the point.
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Spinors in Hilbert Space (Cambridge Tracts in Mathematics)
This item: Spinors in Hilbert Space (Cambridge Tracts in Mathematics)
Price: $139.99
Ships from and sold by Amazon.com