Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field / Moshe Carmeli.

Format:

Book

Author/Creator:

Carmeli, Moshe, 1933-

Language:

English

Subjects (All):

Lorentz transformations.

Transformations (Mathematics).

Physical Description:

1 online resource (411 p.)

Place of Publication:

London : Imperial College Press ; Singapore ; River Edge, NJ : Distributed by World Scientific Pub. Co., c2000.

Language Note:

English

Summary:

This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory.There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups

Contents:

CONTENTS; INTRODUCTION; CHAPTER ONE THE ROTATION GROUP; 1-1 THE THREE-DIMENSIONAL PURE ROTATION GROUP; The Euler Angles; 1-2 THE GROUP SU2; The Groups O3 and SU2; Homomorphism of the Group SU2 onto the Group O3; 1-3 INVARIANT INTEGRALS OVER THE GROUPS O3 AND SU2; Invariant Integral over the Group O3; Invariant integral over the Group SU2; 1-4 REPRESENTATIONS OF THE GROUPS O3 AND SU2; Single- and Double-Valued Representations; Infinitesimal Generators; Canonical Basis; 1-5 MATRIX ELEMENTS OF IRREDUCIBLE REPRESENTATIONS; Spinor Representation of the Group SU2

Matrix Elements of the Operator D(u)Properties of the Matrices Dj(u); Orthogonality Relation; 1-6 DIFFERENTIAL OPERATORS OF INFINITESIMAL ROTATIONS; Representations of O3 in Space of Functions; The Basic Infinitesimal Operators; Angular Momentum Operators; PROBLEMS; CHAPTER TWO THE LORENTZ GROUP; 2-1 INFINITESIMAL LORENTZ MATRICES; Galilean Group; Poincare Group; Proper, Orthochronous, Lorentz Group; Infinitesimal Lorentz Matrices; Commutation Relations; 2-2 INFINITESIMAL OPERATORS; One-parameter Group of Operators

Decomposition of a Representation of the Group SU2 into Irreducible RepresentationsFurther Assumptions; Commutation Relations; 2-3 REPRESENTATIONS OF THE GROUP L; Canonical Basis; Unitarity Conditions; PROBLEMS; CHAPTER THREE SPINOR REPRESENTATION OF THE LORENTZ GROUP; 3-1 THE GROUP SL(2, C) AND THE LORENTZ GROUP; The Group SL(2, C); Homomorphism of the Group SL(2, C) on the Group L; Kernel of Homomorphism; Subgroups of the Group SL(2, C); Connection with Lobachevskian Motion; 3-2 SPINOR REPRESENTATION OF THE GROUP SL(2, C); Spinor Representation in Space of Polynomials

Two-Component SpinorsSpinor Representation by means of the Group SU2; Matrix Elements of the Spinor Operator D(g); 3-3 INFINITESIMAL OPERATORS OF THE SPINOR REPRESENTATION; One-parameter Subgroups; Infinitesimal Operators; Further Properties of Spinor Representations; PROBLEMS; CHAPTER FOUR PRINCIPAL SERIES OF REPRESENTATIONS OF SL(2, C); 4-1 LINEAR SPACES OF REPRESENTATIONS; The Hilbert Space L2(Z); The Hilbert Space L2(SU2); The Hilbert Space L22s(SU2); Fourier Transform on the Group SU2; The Hilbert Space l22s; Linear Spaces of Homogeneous Functions; Other Realizations of the Space D(χ)

4-2 THE GROUP OPERATORSRepresentation of SL(2, C) on D(χ); Other Realizations for D(g; χ); Conjugate Representations; Realization of the Representation of the Principal Series; 4-3 SU2 DESCRIPTION OF THE PRINCIPAL SERIES; Properties of the Principal Series; Realization of the Principal Series by Means of the Group SU2; Realization of the Principal Series in the Space l22s; The Principal Series as a Representation for the Group SU2; Functions on the Group SL(2, C); 4-4 COMPARISON WITH THE INFINITESIMAL APPROACH; Comparison of the Parameters (s, ρ) and (j0, c)

Tangent Space to the Group SL(2, C)

Notes:

Originally published: New York : McGraw-Hill, c1977.

Includes bibliographical references (p. 343-375) and index.

ISBN:

9781848160187

1848160186