Progress in Mathematical Physics

3-D Spinors, Spin-Weighted Functions and their Applications

Authors: Torres del Castillo, Gerardo F.

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About this Textbook

This systematic and self-contained treatment of the theory of three-dimensional spinors and their applications fills an important gap in the literature. Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, spinors are developed in this work for three-dimensional spaces in a language analogous to the spinor formalism used in relativistic spacetime.

Unique features of this work:

* Systematic, coherent exposition throughout

* Introductory treatment of spinors, requiring no previous knowledge of spinors or advanced knowledge of Lie groups

* Three chapters devoted to the definition, properties and applications of spin-weighted functions, with all background given.

* Detailed treatment of spin-weighted spherical harmonics, properties and many applications, with examples from electrodynamics, quantum mechanics, and relativity

* Wide range of topics, including the algebraic classification of spinors, conformal rescalings, connections with torsion and Cartan's structural equations in spinor form, spin weight, spin-weighted operators and the geometrical meaning of the Ricci rotation coefficients

* Bibliography and index

This work will serve graduate students and researchers in mathematics and mathematical and theoretical physics; it is suitable as a course or seminar text, as a reference text, and may also be used for self-study.

Reviews

"In summary…the book gathers much of what can be done with 3-D spinors in an easy-to-read, self-contained form designed for applications that will supplement many available spinor treatments. The book…should be appealing to graduate students and researchers in relativity and mathematical physics."

—Mathematical Reviews

"The presnet book provides an easy-to-read and unconventional presentation of the spinor formalism for three-dimensional spaces with a definite or indefinite metric...Following a nice and descriptive introduction chapters 2-4 are devoted to spin-weighted functions and their applications, while chapters 5 and 6 collect all the standard material on spinor algebra and spinor analysis respectively. The final chapter contains some applications of the formalism to general relativity." ---Monatshefte für Mathematik


Table of contents (7 chapters)

  • Rotations and Spinors

    Torres del Castillo, G. F.

    Pages 1-36

  • Spin-Weighted Spherical Harmonics

    Torres del Castillo, G. F.

    Pages 37-58

  • Spin-Weighted Spherical Harmonics. Applications

    Torres del Castillo, G. F.

    Pages 59-109

  • Spin-Weighted Cylindrical Harmonics

    Torres del Castillo, G. F.

    Pages 111-149

  • Spinor Algebra

    Torres del Castillo, G. F.

    Pages 151-175

Buy this book

eBook $79.99
price for USA (gross)
valid through November 5, 2017
  • ISBN 978-0-8176-8146-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $105.00
price for USA
valid through November 5, 2017
  • ISBN 978-0-8176-3249-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $105.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4612-6416-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
3-D Spinors, Spin-Weighted Functions and their Applications
Authors
Series Title
Progress in Mathematical Physics
Series Volume
32
Copyright
2003
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-8146-3
DOI
10.1007/978-0-8176-8146-3
Hardcover ISBN
978-0-8176-3249-6
Softcover ISBN
978-1-4612-6416-3
Series ISSN
1544-9998
Edition Number
1
Number of Pages
IX, 249
Topics