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.
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1 | (7) |
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2 Special relativity and electromagnetism |
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8 | (15) |
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9 | (5) |
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2.2 Relativistic mechanics |
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14 | (4) |
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18 | (5) |
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3 Some elements of general relativity |
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23 | (24) |
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23 | (2) |
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3.2 General coordinates and vectors |
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25 | (4) |
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29 | (4) |
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3.4 The Einstein equations and some of their solutions |
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33 | (4) |
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37 | (3) |
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3.6 The 3 + 1 decomposition |
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40 | (2) |
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42 | (5) |
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4 Hamiltonian mechanics including constraints and fields |
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47 | (15) |
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4.1 Usual mechanics in Hamiltonian form |
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47 | (1) |
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48 | (3) |
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51 | (6) |
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4.4 Totally constrained systems |
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57 | (5) |
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62 | (9) |
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5.1 Kinematical arena and dynamics |
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62 | (4) |
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66 | (5) |
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6 Quantum mechanics and elements of quantum field theory |
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71 | (20) |
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71 | (5) |
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6.2 Elements of quantum field theory |
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76 | (5) |
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6.3 Interacting quantum field theories and divergences |
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81 | (5) |
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86 | (5) |
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7 General relativity in terms of Ashtekar's new variables |
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91 | (13) |
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91 | (1) |
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7.2 Ashtekar's variables: classical theory |
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92 | (5) |
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97 | (1) |
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98 | (6) |
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8 Loop representation for general relativity |
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104 | (20) |
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8.1 The loop transform and spin networks |
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104 | (6) |
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110 | (7) |
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8.3 The Hamiltonian constraint |
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117 | (7) |
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9 An application: loop quantum cosmology |
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124 | (10) |
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124 | (3) |
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9.2 Traditional Wheeler-De Witt quantization |
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127 | (1) |
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9.3 Loop quantum cosmology |
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128 | (2) |
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9.4 The Hamiltonian constraint |
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130 | (1) |
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131 | (3) |
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134 | (34) |
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134 | (11) |
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10.2 The master constraint and uniform discretizations |
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145 | (4) |
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149 | (7) |
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10.4 Possible observational effects? |
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156 | (7) |
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163 | (5) |
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11 Open issues and controversies |
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168 | (6) |
| References |
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174 | (7) |
| Index |
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181 | |
Rodolfo Gambini did his undergraduate work at the University of the Republic of Uruguay, went for a Ph.D. at the University of Paris and joined the faculty at the Universidad Simon Bolivar in Venezuela. He returned to Uruguay in 1997 where he has been director of several government funding agencies in addition to being a Professor at the University of the Republic. He has won the Trieste Prize in Physics, the presidential prize for scientific accomplishment in Uruguay and received an honorary doctorate from the University of the Republic.
Jorge Pullin did his undergraduate work at the Instituto Balseiro in Bariloche, Argentina, did his Ph.D. thesis work at the University of Cordoba and moved as a post-doc to Syracuse University and the University of Utah. He became a faculty member at PennState and in 2001 joined the Louisiana State University as the Horace Hearne Chair in Theoretical Physics. He is the co-director of the Horace Hearne Institute of Theoretical Physics and the former co-director of the Center for Computation and Technology at the Louisiana State University. He was the chair of the Topical Group in Gravitation of the American Physical Society and served on the editorial boards of Classical and Quantum Gravity and the New Journal of Physics. He is currently on the board of Living Reviews, Papers in Physics, is managing editor of International Journal of Modern Physics D and founding editor of Physical Review X.
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