Del i serien Progress in Mathematical Physics

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

Inbunden, Engelska, 2003

AvGerardo F. Torres del Castillo

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This systematic and self-contained treatment of the theory of three-dimensional spinors and their applications fills an important gap in the literature. Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, spinors are developed in this work for three-dimensional spaces in a language analogous to the spinor formalism used in relativistic spacetime.This work will serve graduate students and researchers in mathematics and mathematical and theoretical physics; it is suitable as a course or seminar text, as a reference text, and may also be used for self-study.

Produktinformation

Utgivningsdatum2003-07-25
Mått155 x 235 x 19 mm
Vikt565 g
FormatInbunden
SpråkEngelska
SerieProgress in Mathematical Physics
Antal sidor249
Upplaga2003
FörlagBirkhauser Boston Inc
ISBN9780817632496

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Fysik inom Naturvetenskap och teknik

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.

"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 fur Mathematik