# Gravitation and Gauge Symmetries

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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

Preface

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

Dynamics

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

Supersymmetry

Representations of supersymmetry

Supergravity

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

Appendices

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

Bibliography

Notations and Conventions

Index

## Reviews

"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."