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|a 9780817649845
|9 978-0-8176-4984-5
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|a 10.1007/978-0-8176-4984-5
|2 doi
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|a 512.55
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|a 512.482
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|a Torres del Castillo, Gerardo F.
|e author.
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|a Spinors in Four-Dimensional Spaces
|c by Gerardo F. Torres del Castillo.
|h [electronic resource] /
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|a 1.
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| 264 |
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|a Boston, MA :
|b Birkhũser Boston :
|b Imprint: Birkhũser,
|c 2010.
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| 300 |
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|a VIII, 177p.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
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|a text file
|b PDF
|2 rda
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| 490 |
1 |
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|a Progress in Mathematical Physics ;
|v 59
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| 505 |
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|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<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.
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|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<U+0013>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 (+ + + <U+0012>) 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. <U+0014>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. <U+0014>Monatshefte f<U+00fc>r Mathematik
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|a Mathematics.
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|a Topological Groups.
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| 650 |
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|a Mathematical physics.
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|a Mathematics.
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| 650 |
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|a Topological Groups, Lie Groups.
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| 650 |
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|a Mathematical Methods in Physics.
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| 650 |
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|a Classical and Quantum Gravitation, Relativity Theory.
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| 650 |
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|a Applications of Mathematics.
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
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|t Springer eBooks
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| 776 |
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8 |
|i Printed edition:
|z 9780817649838
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| 830 |
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|a Progress in Mathematical Physics ;
|v 59
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| 856 |
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|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4984-5
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| 912 |
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|a ZDB-2-PHA
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| 950 |
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|a Physics and Astronomy (Springer-11651)
|