front-matter
Chapter 1
1 Quantum Theory and the Gravitational Field
2 Approaches to Quantum Gravity
3 Quantum Black Holes and Quantum Cosmology
4 Semiclassical Approximation and Decoherence
Chapter 2
1 Introduction and Motivation
2 Canonical Quantisation
2.1 The Classical Stage
2.2 De.ning ‘Canonical Quantisation’
2.3 The Theorem of Groenewold and van Howe
2.4 Discussion
2.5 The Role of the Irreducibility-Postulate
3 Constrained Systems
Appendix 1: Geometry of Hamiltonian Systems
Appendix 2: The Lie Algebra of sl(2, R) and the Absence of Non-trivial, Finite-Dimensional Representations by Anti-unitary Matrices
Chapter 3
1 Motivation and Introduction
1.1 Motivation
1.2 Introduction: Classical Canonical Formulation of General Relativity
1.3 Canonical Quantization Programme for Theories with Constraints
2 Mathematical and Physical Foundations of Quantum General Relativity
2.1 Mathematical Foundations
2.2 Quantum Kinematics
3 Selected Areas of Current Research
3.1 Quantum Dynamics
3.2 Loop Quantum Cosmology
3.3 Path Integral Formulation: Spin Foam Models
3.4 Quantum Black Holes
3.5 Semiclassical Analysis
3.6 Gravitons
4 Selection of Open Research Problems
Chapter 4
1 Introduction
2 Quantum Gravity from Dynamical Triangulations
3 Brief Summary of Discrete Gravitational Path Integrals
4 Geometry from Simplices
5 Lorentzian Nature of the Path Integral
5.1 In Two Dimensions
5.2 In Three Dimensions
5.3 Beyond Three Dimensions
6 Brief Conclusion
Chapter 5
1 Introductory Remarks
2 Free Bosonic Strings
2.1 Classical Bosonic Strings
2.2 Quantized Bosonic Strings
2.3 Further Reading
3 Interacting Bosonic Strings
3.1 Heuristic Discussion
3.2 Vertex Operators
3.3 Interactions in the Path Integral Formalism
3.4 Strings in Curved Backgrounds
3.5 Effective Actions
3.6 Interacting Open and Non-oriented Strings
3.7 Further Reading
4 Supersymmetric Strings
4.1 The RNS Model
4.3 Heterotic Strings
Chapter 6
1 Introduction
2 Gauge-Invariant Method in the Canonical Theory of Generally Covariant Systems
2.1 Space of Solutions, Gauge Group, and Asymptotic Symmetries
2.2 Phase Space
2.3 Observables and Dynamical Symmetries
2.4 Transversal Surfaces
3 A Model: Gravitating Shell
3.1 Space of Solutions, Gauge Group, and Asymptotic Symmetries
3.2 Canonical Theory
4 Quantum Theory
4.1 Group Quantization
4.2 Motion of Wave Packets
4.3 Grey Horizons
4.4 Concluding Remarks
Chapter 7
1 Introduction
2 Historical Overview
3 PBHs as a Probe of Primordial Inhomogeneities
4 PBHs as Probe of Cosmological Phase Transitions
4.1 Soft Equation of State
4.2 Collapse of Cosmic Loops
4.3 Bubble Collisions
4.4 Inflation
5 PBHs as a Probe of a Varying Gravitational Constant
6 PBHs as a Probe of Gravitational Collapse
7 PBHs as a Probe of High Energy Physics
7.1 Gamma-Rays
7.2 Antiprotons
7.3 PBH Explosions
8 PBHs as a Probe of Quantum Gravity
9 Conclusions
Chapter 8
1 Introduction
2 The Assignment of Entropy
3 The Schrödinger Black Hole
4 The Problem and the Lessons
Chapter 9
1 Introduction
1.1 Small Dimensions
1.2 Supersymmetry Breaking and TeV Dimensions
1.3 String Dualities
1.4 The Universe on a Membrane
1.5 New versus Old Models
2 Hiding Extra Dimensions
2.1 Compacti.cation on Tori and Kaluza–Klein States
2.2 Orbifolds and Localized States
3 Low-Scale Strings
3.1 Type I String Theory and D-Branes
4 Gravity Modi.cation and Sub-millimeter Forces
5 Conclusions
Chapter 10
1 A Quantum System
2 Limits for Non-Newtonian Interaction Below 10 µm
3 The Experiment at the Institut Laue-Langevin
3.1 From Hot to Ultracold
3.2 The Setup
4 Gravity and Quantum Mechanics Work Together
4.1 Theoretical Description
4.2 Observation of Quantum States
5 Summary
Chapter 11
1 Introduction
2 The Einstein Equivalence Principle
3 Implications of the Einstein Equivalence Principle
3.1 Matter
3.2 The Gravitational Field
4 Models Which Violate the Einstein Equivalence Principle
4.1 Quantum Gravity Induced Violations of the EEP
4.2 LLI Violations from Non-commutative Geometry
4.3 General Models Violating EEP
5 Experimental Tests of the Einstein Equivalence Principle
5.1 Test of the Universality of Free Fall
5.2 Test of the Universality of the Gravitational Redshift
5.3 Test of Local Lorentz Invariance
6 New Experimental Devices and Developments
6.1 Atom Interferometry
6.2 Atomic Clocks
6.3 Ultrastable Cavities
6.4 Frequency Comb
7 EEP and Modern Metrology
7.1 Ideal Rods and Clocks
7.2 The System of Units
7.3 Consequences of a Violation of the EEP
8 Conclusion