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...
Enregistré dans:
| Hovedforfatter: | |
|---|---|
| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Udgivelse: | 1. |
| Serier: | Progress in Mathematical Physics
59 |
| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Kommentar: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Spinors in four-dimensional spaces, Gerardo F. Torres del Castillo, New York, Birkhäuser, 2010, 1 vol (VIII-177 p.), Progress in mathematical physics, 978-0-8176-4983-8 • Spinors in Four-Dimensional Spaces, Texte imprimé, 9780817649852 |
Indholdsfortegnelse:
- 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