Gerardo F. Torres del Castillo

Spinors in Four-Dimensional Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. 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.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 177
• Erscheinungstermin: 23. Juli 2010
• Englisch
• ISBN-13: 9780817649845
• Artikelnr.: 37346392

Inhaltsangabe

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.

Rezensionen

From the reviews:

"This is a very welcome addition to the bookshelves of those for whom it is mainly intended: graduate students and more experienced researchers using spinors in relativity or quantum field theory. It is a detailed and careful explanation, beginning with the important algebraic steps, and pushing carefully onward to the use of spinors to make powerful results in these fields of physics much easier to obtain. ... This is definitely a book I will be very happy to have on my shelves ... ." (J. D. Finley, III, Mathematical Reviews, Issue 2011 g)

"This book contains an elementary and essentially self-contained exposition of the two-component spinor formalism for a four-dimensional space-time having an arbitrary signature without appealing to the Clifford algebra methodology. ... Each chapter includes numerous examples, and exercises, which make it ideal for the use as a textbook, a reference, or for independent study. It is a notable and welcome addition to the existing literature." (Joseph D. Zund, Zentralblatt MATH, Vol. 1206, 2011)