A first course in loop quantum gravity / Rodolfo Gambini and Jorge Pullin.

Format:

Book

Author/Creator:

Gambini, Rodolfo.

Contributor:

Pullin, Jorge.

Language:

English

Subjects (All):

Quantum gravity.

Physical Description:

viii, 183 pages : illustrations ; 26 cm

Place of Publication:

Oxford ; New York : Oxford University Press, 2011.

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. Book jacket.

Contents:

1 Why quantize gravity? 1

2 Special relativity and electro-magnetism 8

2.1 Space and space-time 9

2.2 Relativistic mechanics 14

2.3 Maxwell theory 18

3 Some elements of general relativity 23

3.1 Introduction 23

3.2 General coordinates and vectors 25

3.3 Curvature 29

3.4 The Einstein equations and some of their solutions 33

3.5 Diffeomorphisms 37

3.6 The 3 + 1 decomposition 40

3.7 Triads 42

4 Hamiltonian mechanics including constraints and fields 47

4.1 Usual mechanics in Hamiltonian form 47

4.2 Constraints 48

4.3 Field theories 51

4.4 Totally constrained systems 57

5 Yang-Mills theories 62

5.1 Kinematical arena and dynamics 62

5.2 Holonomies 66

6 Quantum mechanics and elements of quantum field theory 71

6.1 Quantization 71

6.2 Elements of quantum field theory 76

6.3 Interacting quantum field theories and divergences 81

6.4 Renormalizability 86

7 General relativity in terms of Ashtekar's new variables 91

7.1 Canonical gravity 91

7.2 Ashtekar's variables: classical theory 92

7.3 Coupling to matter 97

7.4 Quantization 98

8 Loop representation for general relativity 104

8.1 The loop transform and spin networks 104

8.2 Geometric operators 110

8.3 The Hamiltonian constraint 117

9 An application: loop quantum cosmology 124

9.1 The classical theory 124

9.2 Traditional Wheeler-De Witt quantization 127

9.3 Loop quantum cosmology 128

9.4 The Hamiltonian constraint 130

9.5 Semiclassical theory 131

10 Further developments 134

10.1 Black hole entropy 134

10.2 The master constraint and uniform discretizations 145

10.3 Spin foams 149

10.4 Possible observational effects? 156

10.5 The problem of time 163

11 Open issues and controversies 168.

Notes:

Includes bibliographical references (pages [174]-179) and index.

ISBN:

0199590753

9780199590759

OCLC:

730413861

Publisher Number:

99945825605