A First Course in Loop Quantum Gravity

by Gambini, Rodolfo; Pullin, Jorge

• ISBN13: 9780199590759
• ISBN10: 0199590753
• Format: Hardcover
• Copyright: 2011-11-01
• Publisher: Oxford University Press

Summary

This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.

Author Biography

Rodolfo Gambini is Professor of Physics at the University of the Republic of Uruguay. Jorge Pullin is Horace Hearne Chair in Theoretical Physics at the Louisiana State University.

Table of Contents

Why quantize gravity?	p. 1
Special relativity and electro-magnetism	p. 8
Space and space-time	p. 9
Relativistic mechanics	p. 14
Maxwell theory	p. 18
Some elements of general relativity	p. 23
Introduction	p. 23
General coordinates and vectors	p. 25
Curvature	p. 29
The Einstein equations and some of their solutions	p. 33
Diffeomorphisms	p. 37
The 3 + 1 decomposition	p. 40
Triads	p. 42
Hamiltonian mechanics including constraints and fields	p. 47
Usual mechanics in Hamiltonian form	p. 47
Constraints	p. 48
Field theories	p. 51
Totally constrained systems	p. 57
Yang-Mills theories	p. 62
Kinematical arena and dynamics	p. 62
Holonomies	p. 66
Quantum mechanics and elements of quantum field theory	p. 71
Quantization	p. 71
Elements of quantum field theory	p. 76
Interacting quantum field theories and divergences	p. 81
Renormalizability	p. 86
General relativity in terms of Ashtekar's new variables	p. 91
Canonical gravity	p. 91
Ashtekar's variables: classical theory	p. 92
Coupling to matter	p. 97
Quantization	p. 98
Loop representation for general relativity	p. 104
The loop transform and spin networks	p. 104
Geometric operators	p. 110
The Hamiltonian constraint	p. 117
An application: loop quantum cosmology	p. 124
The classical theory	p. 124
Traditional Wheeler-De Witt quantization	p. 127
Loop quantum cosmology	p. 128
The Hamiltonian constraint	p. 130
Semiclassical theory	p. 131
Further developments	p. 134
Black hole entropy	p. 134
The master constraint and uniform discretizations	p. 145
Spin foams	p. 149
Possible observational effects?	p. 156
The problem of time	p. 163
Open issues and controversies	p. 168
References	p. 174
Index	p. 181
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