Towards Quantum Gravity: Proceedings of the XXXV International Winter School on Theoretical Physics Held in Polanica, Poland, 2–11 February 1999 (Lecture Notes in Physics, 541)

Chapter 1
	1 Introduction
	2 First the conclusions: what has this phenomenology achieved?
	3 Addendum to conclusions: any hints to theorists from experiments?
	4 Interferometry and fuzzy space-time
		4.1 Operative definition of fuzzy distance
		4.2 Random-walk noise from random-walk models of quantum space-time fluctuations
		4.3 Comparison with gravity-wave interferometer data
		4.4 Less noisy random-walk models of distance fluctuations?
	5 Gamma-ray bursts and in-vacuo dispersion
	6 Other quantum-gravity experiments
		6.1 Neutral kaons and CPT violation
		6.2 Interferometry and string cosmology
		6.3 Matter interferometry and primary state diffusion
		6.4 Colliders and large extra dimensions
	7 Classical-space-time-induced quantum phases in matter interferometry
	8 Estimates of space-time fuzziness from measurability bounds
		8.1 Minimum-length noise
		8.2 Random-walk noise motivated by the analysis of a Salecker-Wigner gedanken experiment
		8.3 Random-walk noise mot vated by linear deformation of dispersion relation
		8.4 Noise motivated by quadratic deformation of dispersion relation
		8.5 Noise with f-5/6 amplitude spectral density
	9 Relations with other quantum gravity approaches
		9.1 Canonical Quantum Gravity
		9.2 Critical and non-critical strong theories
		9.3 Other types of measurement analyses
	10 Quantum gravity, no strings attached
		10.1 A low-energy effective theory of quantum gravity
		10.2 Theories on non-commutative Minkowski space-time
	11 Conservative motivation and other closing remarks
	Acknowledgements
	References
Chapter 2
	1 Motivation
	2 Key Issues
	3 Summary
		3.1 Isolated horizons
		3.2 Mechanics
		3.3 Quantum geometry in the bulk
		3.4 Quantum geometry of horizon and entropy
	4 Discussion
	References
Chapter 3
	References
Chapter 4
	1 Introduction
	2 Supersymmetry and anti-de Sitter space
	3 Anti-de Sitter supersymmetry and masslike terms
	4 The quadratic Casimir operator
	5 Unitar representations of the anti-de Sitter algebra
	6 The oscillator construction
	7 The superalgebra OSp(1 | 4)
	8 Conclusions
	References
Chapter 5
	1 Introduction
	2 Combinatorial descriptions of quantum spacetime
		2.1 Combinatoria description of spatial geometry
		2.2 Causal evolution of quantum geometries
		2.3 How the dynamics are specified
	3 The problem of the classical limit and its relationship to critical phenomena
	4 Is there quantum directed percolation?
	5 Discrete superspace and its structure
	6 Some simple models
	7 The classical limit of the frozen models
	8 Dynamics including the parameters
	9 A new approach to the problem of time
		9.1 The argument for the absence of time
		9.2 A problem with the argument for the disappearance of time
		9.3 Can we do physics without a constructible state space?
		9.4 Implications
	Acknowledgements
	References
Chapter 6
	1 Deformations of space-time and phase space geometries
	2 Why the coordinates should not commute at Planck\'s scale
	3 Non-commutative differential geometry
	4 Non-commutative analog of Kaluza-Klein and gauge theories
	5 Minkowskian space-time as a commutative limit
	6 Quantum spaces and quantum groups
	7 Conclusion
	References
Chapter 7
	1 Introduct on
	2 Lessons from quantum theory
		2.1 Superposition principle and “measurements”
		2.2 Decoherence: Concepts, examples, experiments
		2.3 O the interpretation of quantum theory
	3 Quantum cosmology
		3.1 Why spacetime cannot be classical
		3.2 Problem of time
		3.3 Role of boundary conditions
	4 Emergence of a classical world
		4.1 Semiclassical approximation to quantum gravity
		4.2 Decoherence in quantum cosmology
		4.3 Classicality of primordial fluctuations
	5 Acknowledgements
	References
Chapter 8
	1 Introduction
	2 Kruskal Manifold and the RP 3 Geon
	3 Vacua on Kruskal and on the RP 3 Geon
	4 Entropy of the RP 3 Geon?
	5 AdS3, the Spinless Nonextremal BTZ Hole, and the RP2 Geon
		5.1 AdS3, its Covering Space, and the Conformal Boundary
		5.2 The Spinless Nonextremal BT Hole
		5.3 The RP 2 Geon
	6 Vacua on the Conformal Boundaries
	7 Holography and String Theory
	8 Concluding Remarks
	References
Chapter 9
	References
Chapter 10
	1 Introduction
	2 The meaning of noncommutative geometry
		2.1 Curvature in momentum space – a possible new force of nature
		2.2 Algebraic structure of quantum mechanics
		2.3 Principle of representation-theoretic self-duality
		2.4 Relative realism
	3 Fourier theory
		3.1 Loop variables and Fourier duality
		3.2 No Abelia Fourier Transform
	4 Bicrossproduct model of Planck-scale physics
		4.1 The Planck-scale quantum group
		4.2 Higher dimensional analogue
		4.3 General construction
	5 Deformed quantum enveloping algebras
		5.1 Braided mathematics and braided groups
		5.2 Systematic q-Special Relativity
		5.3 The physical meaning of q
	6 Noncommutative differential geometry and Riemannian manifolds
		6.1 Quantum differential forms
		6.2 Bundles and connections
		6.3 Soldering and quantum Riemannian structure
		6.4 Semiclassical limit
	Acknowledgements
	References
Chapter 11
	1 Introduct on
	2 Basic Formalism of Loop Quantum Gravity
		2.1 A brief Outline of the Connection Formalism
		2.2 Basic Defnitions
		2.3 The Construction of a Hilbert Space H
		2.4 A Basis in the Hilbert Space
		2.5 The SU(2) Gauge Constraint
		2.6 Operators on H
	3 Quantization of the Area
	4 The Physical Contents of Quantum Gravity and the Meaning of Diffeomorphism Invariance
		4.1 Passive and Active Diffeomorphism Invariance
		4.2 Dirac Observables
		4.3 The Hole Argument
		4.4 The Physical Interpretation
	5 Dynamics, True Observables and Spin Foams
		5.1 The Diffeomorphism Constraint
		5.2 The Hamiltonian Constraint, Spin Foam, and Physical Observables
	6 Open Problems and Future Perspectives
	References
Chapter 12
	1 Introduction
	2 String theory and dualities
		2.1 Bosonic string and D-branes
		2.2 Superstrings
		2.3 Dualities
	3 Brane solutions
		3.1 M-branes
		3.2 Intersection rules
	4 Black holes in string theory
		4.1 Extremal black holes and the D-brane counting
		4.2 Non-extremal black holes and the BTZ black hole
		4.3 Low-energy limit and the near-horizon geometry
	Acknowledgments
	References
Chapter 13
	1 Planar gravitational waves
	2 Einstein-scalar waves
	3 Einstein-Dirac waves
	4 Einstein-Maxwell waves
	References