Gravitation and Gauge Symmetries  book cover
1st Edition

Gravitation and Gauge Symmetries

ISBN 9780750307673
Published October 25, 2001 by CRC Press
536 Pages

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Book Description

In the course of the development of electromagnetic, weak and strong interactions, the concept of (internal) gauge invariance grew up and established itself as an unavoidable dynamical principle in particle physics. It is less known that the principle of equivalence, and the basic dynamical properties of the gravitational interaction can also be expressed as a (spacetime) gauge symmetry.

Gravitation and Gauge Symmetries sheds light on the connection between the intrinsic structure of gravity and the principle of gauge invariance, which may lead to a consistent unified field theory. The first part of the book gives a systematic account of the structure of gravity as a theory based on spacetime gauge symmetries. Some basic properties of space, time, and gravity are reviewed in the first, introductory chapter. The next chapter deals with elements of global Poincaré and conformal symmetries, which are necessary for the exposition of their localizations; the structure of the corresponding gauge theories of gravity is explored in chapters 3 and 4. Then, in chapters 5 and 6, we present the basic features of the constrained Hamiltonian of Poincaré gauge theory, discuss the relation between gauge symmetries and conservation laws, and introduce the concept of gravitational energy and other conserved quantities. The second part of the book explores the most promising attempts to build a unified field theory containing gravity, on the basis of the gauge principle. The author presents the possibility to constrict the theory of gravity as a nonlinear field theory in flat spacetime. The final chapters yield an exposition of the ideas of supersymmetry and supergravity, Kaluza-Klein theory, and string theory.

Gravitation and Gauge Symmetries will be of interest to postgraduate students and researchers in gravitation, high energy physics and mathematical physics.

Table of Contents


Space, Time and Gravitation
Relativity of space and time
Gravitation and geometry

Spacetime Symmetries
Poincaré symmetry
Conformal symmetry

Poincaré Gauge Theory
Poincaré gauge invariance
Geometric interpretation
Gravitational dynamics

Weyl Gauge Theory
Weyl gauge invariance
Weyl-Cartan geometry

Hamiltonian Dynamics
Constrained Hamiltonian dynamics
The gravitational Hamiltonian
Specific models

Symmetries and Conservation Laws
Gauge symmetries
Conservation laws-EC theory
Conservation laws-the teleparallel theory
Chern-Simons gauge theory in D = 3

Gravity in Flat Spacetime
Theories of long range forces
Attempts to build a realistic theory

Nonlinear Effects in Gravity
Nonlinear effects in Yang-Mills theory
Scalar theory of gravity
Tensor theory of gravity
The first order formalism

Supersymmetry and Supergravity
Representations of supersymmetry

Kaluza-Klein Theory
Basic ideas
Five-dimensional KK theory
Higher-dimensional KK theory

String Theory
Classical bosonic strings
Oscillator formalism
First quantization
Covariant field theory
General remarks

A: Local internal symmetries
B: Differentiable manifolds
C: De Sitter gauge theory
D: The scalar-tensor theory
E: Ashtekar's formulation of GR
F: Constraint algebra and gauge symmetries
G: Covariance, spin and interaction of massless particles
H: Lorentz group and spinors
I: Poincaré group and massless particles
J: Dirac matrices and spinors
K: Symmetry groups and manifolds
L: Chern-Simons gravity in three dimensions
M: Fourier expansion

Notations and Conventions

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"The book is very well written. It provides a very good pedagogical survey of the gravity from the point of view of gauge theories that are very successful in explaining the other physical interactions. Basic ideas of the most recent theories of unification of all fundamental physical interactions are explored in an effective way. The book contains very useful examples and exercises making understanding of presented ideas easier, and they extend the results discussed in the text.
- Zdenek Stuchlik, Acta Physica Slovaca

"The experience and maturity of the writer are manifest in the clear and pedagogical style of exposition. The subject is a difficult one and the going is tough, but the author does an excellent job of making the topics as digestible as possible, without sacrifice of detail and rigor. Mathematical propriety is maintained, and at the same time there are many illuminations of physical intuition, essential to keep the interest of the physicist alive … the book is an excellent introduction to the general area of gauge symmetries and gravity …. this volume is handsomely produced and printed on good quality paper, making a pleasant and useful addition to a theoretician's library."
- Lewis Ryder, University of Kent at Canterbury, UK

"This book is a rather broad scope, intending to shed light upon the intrinsic structure of gravity and gauge invariance … This book is accompanied by 13 useful appendices, which give, inter alia, some more details on the de Sitter gauge theory, the Ashtekar reformulation of general relativity, and Chern-Simons models in three dimensions ... Certainly, Milutin Blagojevic's book fills a gap in the current literature and will be useful for students and researchers of gravity."