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

1. Front Matter

   Pages i-ix

   PDF

2. Rotations and Spinors

   • G. F. Torres del Castillo

   Pages 1-36

3. Spin-Weighted Spherical Harmonics

   • G. F. Torres del Castillo

   Pages 37-58

4. Spin-Weighted Spherical Harmonics. Applications

   • G. F. Torres del Castillo

   Pages 59-109

5. Spin-Weighted Cylindrical Harmonics

   • G. F. Torres del Castillo

   Pages 111-149

6. Spinor Algebra

   • G. F. Torres del Castillo

   Pages 151-175

7. Spinor Analysis

   • G. F. Torres del Castillo

   Pages 177-214

8. Applications to General Relativity

   • G. F. Torres del Castillo

   Pages 215-234

9. Back Matter

   Pages 235-249

   PDF

The spinor calculus employed in general relativity is a very useful tool; many expressions and computations are considerably simplified if one makes use of spinors instead of tensors. Some advantages of the spinor formalism applied in the four-dimensional space-time of general relativity come from the fact that each spinor index takes two values only, which simplifies the algebraic manipulations. Spinors for spaces of any dimension can be defined in connection with rep­ resentations of orthogonal groups and in the case of spaces of dimension three, the spinor indices also take two values only, which allows us to apply some of the results found in the two-component spinor formalism of four-dimensional space-time. The spinor formalism for three-dimensional spaces has been partially developed, mainly for spaces with a definite metric, also in connection with gen­ eral relativity (e.g., in space-plus-time decompositions of space-time), defining the spinors of three-dimensional space from those corresponding to four-dimensional space-time, but the spinor formalism for three-dimensional spaces considered on their own is not widely known or employed. One of the aims of this book is to give an account of the spinor formalism for three-dimensional spaces, with definite or indefinite metric, and its applications in physics and differential geometry. Another is to give an elementary treatment of the spin-weighted functions and their various applications in mathematical physics.

• Albert Einstein
• EFE
• Relativity
• Theoretical physics
• electrodynamics
• general relativity
• mathematical physics

"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

• Instituto de Ciencias, Universidad Autonoma de Puebla, Puebla, Mexico

  G. F. Torres del Castillo

Policies and ethics