Spinors in Four-Dimensional Spaces

• Κύριος συγγραφέας: Torres del Castillo, Gerardo F. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2010.
• Έκδοση: 1.
• Σειρά: Progress in Mathematical Physics ; 59
• Θέματα: Mathematics.; Topological groups.; Lie groups.; Applied mathematics.; Engineering mathematics.; Physics.; Gravitation.; Topological Groups, Lie Groups.; Mathematical Methods in Physics.; Classical and Quantum Gravitation, Relativity Theory.; Applications of Mathematics.

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...

Πίνακας περιεχομένων:

• 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.