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...
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| Format: | Electronic |
| Language: | English |
| Published: |
Boston, MA :
Birkhũser Boston : Imprint: Birkhũser,
2010.
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| Edition: | 1. |
| Series: | Progress in Mathematical Physics ;
59 |
| Subjects: | |
| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4984-5 |
Table of Contents:
- 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<U+0019>s Equations.-3.2 Dirac<U+0019>s Equation .-3.3 Einstein<U+0019>s Equations.-3.3.1 The Goldberg<U+0013>Sachs Theorem.-3.3.2 Space-Times with Symmetries. Ernst Potentials.-3.4 Killing Spinors.-Exercises.-4 Further Applications.-4.1 Self-Dual Yang<U+0013>Mills Fields.-4.2 H and H H Spaces.-4.3 Killing Bispinors. The Dirac Operator.-Exercises.-A Bases Induced by Coordinate Systems.-References.