Three Roads To Quantum Gravity

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SUGGESTIONS FOR FURTHER READING 237 9808070. The reformulation of the consistent histories formulation in terms of topos theory, which emphasizes its relational aspects, is found in C.J. Isham and J. Butter®eld, `Some possible roles for topos theory in quantum theory and quantum gravity', gr-qc/9910005. Other relational approaches to quantum cosmology are found in L. Crane, Journal of Mathematical Physics 36 (1995) 6180; L. Crane, in Knots and Quantum Gravity, edited by J. Baez (Oxford University Press, New York, 1994); L. Crane, `Categorical physics', hep-th/9301061; F. Markopoulou, `Quantum causal histories', hep-th/9904009, Class. Quan. Grav. 17 (2000) 2059±2072; F. Markopoulou, `An insider's guide to quantum causal histories', hep-th/9912137, Nucl. Phys. Proc. Suppl. 88 (2000) 308±313; C. Rovelli, `Relational quantum mechanics', quant-ph/9609002, International Journal of Theoretical Physics 35 (1996) 1637; L. Smolin, `The Bekenstein bound, topological ®eld theory and pluralistic quantum cosmology', gr-qc/950806. CHAPTER 4 The process formulation of quantum theory was developed ®rst by David Finkelstein, whose work is the main inspiration for this chapter. It is described in David Ritz Finkelstein, Quantum Relativity: A Synthesis of the ideas of Einstein and Heisenberg (Springer-Verlag, 1996). Rafael Sorkin has also pioneered the exploration of the role of causality in quantum gravity. CHAPTERS 5±8 This is all standard material in classical general relativity and quantum ®eld theory. Good introductions are N.D. Birrell and P.C.W. Davies, Quantum Fields in Curved Spacetime (Cambridge University Press, 1982); and Robert M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (University of Chicago Press, 1994). CHAPTERS 9 AND 10 There are several expositions of loop quantum gravity at a semipopular or semi-technical level. They include Carlo Rovelli, `Loop quantum gravity', gr-qc/9710008, Carlo Rovelli, `Quantum spacetime: what do we know?', gr-qc/9903045; L. Smolin in Quantum Gravity and Cosmology, edited by Juan Perez-Mercader et al. (World Scienti®c, 1992); L. Smolin, `The future of spin networks', in The Geometric Universe (1997), edited by S.A. Huggett et al. (Oxford University Press, 1998), gr-qc/9702030. The book by Rodolfo Gambini and Jorge Pullin, Loops, Knots, Gauge Theories and Quantum Gravity (Cambridge University Press, 1996) describes their approach to the subject.
238 THREE ROADS TO QUANTUM GRAVITY The mathematically rigorous approach to loop quantum gravity is presented in Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf, Jose Mourao and Thomas Thiemann, `Quantization of diffeomorphism invariant theories of connections with local degrees of freedom', Journal of Mathematical Physics 36 (1995) 6456, gr-qc/9504018; Abhay Ashtekar, Jerzy Lewandowski, `Quantum ®eld theory of geometry', hep-th/ 9603083; and T. Thiemann, `Quantum spin dynamics I and II', gr-qc/ 9606089, gr-qc/9606090, Classical and Quantum Gravity 15 (1998) 839, 875. The original references for the Ashtekar±Sen formalism are in A. Sen, Physics. Letters B119 (1982) 89; International Journal; of Theoretical Physics 21 (1982) 1; A. Ashtekar, Physical Review Letters 57 (1986) 2244; A. Ashtekar, Physical. Review D36 (1987) 1587. CHAPTER 11 This is all standard material in string theory, to which Brian Greene's The Elegant Universe (Norton, 1999) is an excellent introduction. The best textbook is J. Polchinksi, String Theory (Cambridge University Press, 1998). CHAPTER 12 The original references for the holographic principle are Gerard 't Hooft, `Dimensional reduction in quantum gravity', gr-qc/9310006, in Salanfestschrift, edited by A. Alo, J. Ellis, S. Randjbar-Daemi (World Scienti®c, 1993); and Leonard Susskind, `The world as a hologram', hep-th/9409089, Journal of Mathematical Physics 36 (1995) 6377. Ideas closely related to the holographic principle were presented earlier by L. Crane in `Categorical physics', hep-th/9301061 and hep-th/9308126 in Knots and Quantum Gravity, edited by J. Baez (Oxford University Press, 1994); L. Crane, `Clocks and categories: is quantum gravity algebraic?' Journal of Mathematical Physics 36 (1995) 6180, gr-qc/ 9504038. The Bekenstein bound was proposed in J.D. Bekenstein, Lettere Nuovo Cimento 4 (1972) 737, Physical Review D7 (1973), 2333; Physical Review D9 (1974) 3292. Ted Jacobson's paper deriving general relativity from the Bekenstein bound and the laws of thermodynamics is `Thermodynamics of spacetime: the Einstein equation of state', gr-qc/9504004, Physical Review Letters 75 (1995) 1260. The derivation of the Bekenstein bound in loop quantum gravity is in L. Smolin, `Linking topological quantum ®eld theory and nonperturbative quantum gravity', gr-qc/9505028, Journal of Mathematical Physics 36 (1995) 6417. Another very promising version of the holographic principle was proposed by Rafael Bousso in `A covariant
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CHAPTER 2 .........................
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II WHAT WE HAVE LEARNED
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CHAPTER 7 .........................
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CHAPTER 9 .........................
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CHAPTER 11 ........................
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CHAPTER 12 ........................
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THE HOLOGRAPHIC PRINCIPLE 171 gener
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THE HOLOGRAPHIC PRINCIPLE 173 FIGUR
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THE HOLOGRAPHIC PRINCIPLE 175 the g
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CHAPTER 13 ........................
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HOW TO WEAVE A STRING 181 thing!" I
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HOW TO WEAVE A STRING 183 other. Th
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HOW TO WEAVE A STRING 185 What is r
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Page 216 and 217: EPILOGUE: .........................
Page 218 and 219: EPILOGUE: 209 And quantum gravity i
Page 220 and 221: EPILOGUE: 211 of systems containing
Page 222 and 223: POSTSCRIPT 213 These cosmic rays ar
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Page 226 and 227: POSTSCRIPT 217 light, which is the
Page 228 and 229: POSTSCRIPT 219 This is good news in
Page 230 and 231: POSTSCRIPT 221 But there is a secon
Page 232 and 233: POSTSCRIPT 223 Chopin Soo and Marti
Page 234 and 235: POSTSCRIPT 225 speed of light with
Page 236 and 237: GLOSSARY 227 cannot be greater than
Page 238 and 239: GLOSSARY 229 event In relativity th
Page 240 and 241: GLOSSARY 231 Newton's gravitational
Page 242 and 243: GLOSSARY 233 spin The angular momen
Page 244 and 245: SUGGESTIONS FOR FURTHER READING ...
Page 248 and 249: SUGGESTIONS FOR FURTHER READING 239
Page 250 and 251: INDEX .............................
Page 252 and 253: INDEX 243 black hole, 70, 73±4, 17
Page 254 and 255: INDEX 245 black hole formation, 189
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