3-D Spinors, Spin-Weighted Functions and their Applications

Erscheinungsjahr 2003
ISBN: 978-0-8176-3249-6
Verlag: Birkhäuser

Buch, Englisch, 249 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1210 g

Reihe: Progress in Mathematical Physics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Torres del Castillo, Gerardo F.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Experimentalphysik
• Naturwissenschaften Physik Quantenphysik Relativität, Gravitation
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.