Gerardo F. Torres del Castillo

3-D Spinors, Spin-Weighted Functions and their Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

A systematic, self-contained text that provides an introduction to 3-D spinors & their applications and fills a gap in the literature. Includes detailed treatment of spin-weighted harmonics and many applications from electrodynamics, quantum mechanics, & general relativity. Assumes no previous knowledge of spinors; includes all prerequisites. Ideal for graduate students and researchers, for self-study, courses, or as a reference text.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 249
• Erscheinungstermin: 7. September 2012
• Englisch
• ISBN-13: 9780817681463
• Artikelnr.: 44198681

Autorenporträt

Gerardo F. Torres del Castillo, Universidad Autonoma de Puebla, Mexico

Inhaltsangabe

1 Rotations and Spinors.- 1.1 Representation of the rotations.- 1.2 Spinors.- 1.3 Elementary applications.- 1.4 Spinors in spaces with indefinite metric.- 2 Spin-Weighted Spherical Harmonics.- 2.1 Spherical harmonics.- 2.2 Spin weight.- 2.3 Wigner functions.- 3 Spin-Weighted Spherical Harmonics. Applications.- 3.1 Solution of the vector Helmholtz equation.- 3.2 The source-free electromagnetic field.- 3.3 The equation for elastic waves in an isotropic medium.- 3.4 The Weyl neutrino equation.- 3.5 The Dirac equation.- 3.6 The spin-2 Helmholtz equation.- 3.7 Linearized Einstein theory.- 3.8 Magnetic monopole.- 4 Spin-Weighted Cylindrical Harmonics.- 4.1 Definitions and basic properties.- 4.2 Representation of the Euclidean group of the plane.- 4.3 Applications.- 4.4 Parabolic and elliptic coordinates.- 4.5 Applications.- 5 Spinor Algebra.- 5.1 The spinor equivalent of a tensor.- 5.2 The orthogonal and spin groups.- 5.3 Algebraic classification.- 5.4 The triad defined by a spinor.- 6 Spinor Analysis.- 6.1 Covariant differentiation.- 6.2 Curvature.- 6.3 Spin weight and priming operation.- 6.4 Metric connections with torsion.- 6.5 Congruences of curves.- 6.6 Applications.- 7 Applications to General Relativity.- 7.1 Spacelike hypersurfaces.- 7.2 Timelike hypersurfaces.- 7.3 Stationary space-times.- Appendix: Spinors in the Four-Dimensional Space-Time.- References.

Rezensionen

"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 presnet 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 chapters 2-4 are devoted to spin-weighted functions and their applications, while chapters 5 and 6 collect all the standard material on spinor algebra and spinor analysis respectively. The final chapter contains some applications of the formalism to general relativity." ---Monatshefte für Mathematik