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001 978-0-8176-4984-5
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007 cr nn 008mamaa
008 100721s2010 xxu| s |||| 0|eng d
020 _a9780817649845
_9978-0-8176-4984-5
024 7 _a10.1007/978-0-8176-4984-5
_2doi
050 4 _aQA252.3
050 4 _aQA387
072 7 _aPBG
_2bicssc
072 7 _aMAT014000
_2bisacsh
072 7 _aMAT038000
_2bisacsh
082 0 4 _a512.55
_223
082 0 4 _a512.482
_223
100 1 _aTorres del Castillo, Gerardo F.
_eauthor.
245 1 0 _aSpinors in Four-Dimensional Spaces
_h[electronic resource] /
_cby Gerardo F. Torres del Castillo.
250 _a1.
264 1 _aBoston, MA :
_bBirkhäuser Boston :
_bImprint: Birkhäuser,
_c2010.
300 _aVIII, 177p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematical Physics ;
_v59
505 0 _a1 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.
520 _aWithout 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. Key topics and features: • Uniform treatment of the spinor formalism for four-dimensional spaces of any signature, not only the usual signature (+ + + −) 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. —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. —Monatshefte für Mathematik
650 0 _aMathematics.
650 0 _aTopological Groups.
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aTopological Groups, Lie Groups.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aClassical and Quantum Gravitation, Relativity Theory.
650 2 4 _aApplications of Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817649838
830 0 _aProgress in Mathematical Physics ;
_v59
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4984-5
912 _aZDB-2-PHA
999 _c109930
_d109930