e-book

3-D spinors, spin-weighted functions and their applications

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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 representations 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 general 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.

The best-known example of the spin-weighted functions are the spin-weighted spherical harmonics, which are a generalization of the ordinary spherical harmonics and, as the latter, are very useful in the solution by separation of variables of partial differential equations. By means of the spin-weighted spherical harmonics one can give a unified treatment of fields of any spin, without requiring definitions of the vector, tensor and spinor spherical harmonics employed in electrodynamics, quantum mechanics and general relativity.

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Ketersediaan

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Informasi Detail

Judul Seri

Progress in mathematica1 physics ; v. 20

No. Panggil

-

Penerbit

New York : Springer Science+Business Media New York., 2003

Deskripsi Fisik

QA433.T67 - 515'.63-dc21

Bahasa

English

ISBN/ISSN

978-0-8176-8146-3

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

v. 20

Subjek

FISIKA

Info Detail Spesifik

-

Pernyataan Tanggungjawab

agus

Versi lain/terkait

Lampiran Berkas

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