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Birkhäuser - Birkhäuser Physics | 3-D Spinors, Spin-Weighted Functions and their Applications

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

Torres del Castillo, Gerardo F.

2003, IX, 249 p.

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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.

Content Level » Graduate

Keywords » Albert Einstein - EFE - Relativity - Theoretical physics - electrodynamics - general relativity - mathematical physics

Related subjects » Birkhäuser Mathematics - Birkhäuser Physics

Table of contents 

Preface * Rotations and Spinors * Spin-weighted spherical harmonics * Spin-weighted spherical harmonics with Applications * Spin-weighted cylindrical harmonics * Spinor algebra * Spinor analysis * Applications to general relativity * Appendix: Spinors in four-dimensional space-time * References * Index

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