Author | Torres del Castillo, G. F. author |
---|---|
Title | 3-D Spinors, Spin-Weighted Functions and their Applications [electronic resource] / by G. F. Torres del Castillo |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003 |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8146-3 |
Descript | IX, 249 p. online resource |
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