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Spinors in Four-Dimensional Spaces
Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimen...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston, MA :
Birkhäuser Boston : Imprint: Birkhäuser,
2010.
|
| Edición: | 1st ed. 2010. |
| Colección: | Progress in Mathematical Physics,
59 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-0-8176-4984-5 | ||
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| 100 | 1 | |a Torres del Castillo, Gerardo F. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Spinors in Four-Dimensional Spaces |h [electronic resource] / |c by Gerardo F. Torres del Castillo. |
| 250 | |a 1st ed. 2010. | ||
| 264 | 1 | |a Boston, MA : |b Birkhäuser Boston : |b Imprint: Birkhäuser, |c 2010. | |
| 300 | |a VIII, 177 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 490 | 1 | |a Progress in Mathematical Physics, |x 2197-1846 ; |v 59 | |
| 505 | 0 | |a 1 Spinor Algebra.-1.1 Orthogonal Groups.-1.2 Null Tetrads and the Spinor Equivalent of a Tensor.-1.3 Spinorial Representation of the Orthogonal Transformations.-1.3.1 Euclidean Signature.-1.3.2 Lorentzian Signature.-1.3.3 Ultrahyperbolic Signature.-1.4 Reflections.-1.5 Clifford Algebra. Dirac Spinors.-1.6 Inner Products. Mate of a Spinor.-1.7 Principal Spinors. Algebraic Classification.-Exercises.-2 Connection and Curvature.-2.1 Covariant Differentiation -- 2.2 Curvature.-2.2.1 Curvature Spinors.-2.2.2 Algebraic Classification of the Conformal Curvature.-2.3 Conformal Rescalings.-2.4 Killing Vectors. Lie Derivative of Spinors.-Exercises -- 3 Applications to General Relativity.-3.1 Maxwell's Equations.-3.2 Dirac's Equation .-3.3 Einstein's Equations.-3.3.1 The Goldberg-Sachs Theorem.-3.3.2 Space-Times with Symmetries. Ernst Potentials.-3.4 Killing Spinors.-Exercises.-4 Further Applications.-4.1 Self-Dual Yang-Mills Fields.-4.2 H and H H Spaces.-4.3 Killing Bispinors. The Dirac Operator.-Exercises.-A Bases Induced by Coordinate Systems.-References. | |
| 520 | |a Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang-Mills theory, are derived in detail using illustrative examples. Key topics and features: • Uniform treatment of the spinor formalism for four-dimensional spaces of any signature, not only the usual signature (+ + + −) employed in relativity • Examples taken from Riemannian geometry and special or general relativity are discussed in detail, emphasizing the usefulness of the two-component spinor formalism • Exercises in each chapter • The relationship of Clifford algebras and Dirac four-component spinors is established • Applications of the two-component formalism, focusing mainly on general relativity, are presented in the context of actual computations Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide. Reviews from the author's previous book, 3-D Spinors, Spin-Weighted Functions and their Applications: 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 present 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...the final chapter contains some applications of the formalism to general relativity. -Monatshefte für Mathematik. | ||
| 650 | 0 | |a Topological groups. | |
| 650 | 0 | |a Lie groups. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Gravitation. | |
| 650 | 0 | |a Mathematics. | |
| 650 | 1 | 4 | |a Topological Groups and Lie Groups. |
| 650 | 2 | 4 | |a Mathematical Methods in Physics. |
| 650 | 2 | 4 | |a Classical and Quantum Gravity. |
| 650 | 2 | 4 | |a Applications of Mathematics. |
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| 776 | 0 | 8 | |i Printed edition: |z 9780817649838 |
| 776 | 0 | 8 | |i Printed edition: |z 9780817649852 |
| 830 | 0 | |a Progress in Mathematical Physics, |x 2197-1846 ; |v 59 | |
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