Covariant Loop Quantum Gravity · an Elementary Introduction to Quantum Gravity and Spinfoam Theory (Cambridge Monographs on Mathematical Physics) by Rovelli, Carlo -- Read -- Imperial Library of Trantor

Index

Half-title page Title Copyright Dedication Contents Preface Part I FOUNDATIONS

1 Spacetime as a quantum object

1.1 The problem 1.2 The end of space and time 1.3 Geometry quantized 1.3.1 Quanta of area and volume 1.4 Physical consequences of the existence of the Planck scale 1.4.1 Discreteness: scaling is finite 1.4.2 Fuzziness: disappearance of classical space and time 1.5 Graphs, loops, and quantum Faraday lines 1.6 The landscape 1.7 Complements 1.7.1 SU(2) representations and spinors 1.7.2 Pauli matrices 1.7.3 Eigenvalues of the volume

2 Physics without time

2.1 Hamilton function 2.1.1 Boundary terms 2.2 Transition amplitude 2.2.1 Transition amplitude as an integral over paths 2.2.2 General properties of the transition amplitude 2.3 General covariant form of mechanics 2.3.1 Hamilton function of a general covariant system 2.3.2 Partial observables 2.3.3 Classical physics without time 2.4 Quantum physics without time 2.4.1 Observability in quantum gravity 2.4.2 Boundary formalism 2.4.3 Relational quanta, relational space 2.5 Complements 2.5.1 Example of a timeless system 2.5.2 Symplectic structure and Hamilton function

3 Gravity

3.1 Einstein’s formulation 3.2 Tetrads and fermions 3.2.1 An important sign 3.2.2 First-order formulation 3.3 Holst action and Barbero–Immirzi coupling constant 3.3.1 Linear simplicity constraint 3.3.2 Boundary term 3.4 Hamiltonian general relativity 3.4.1 ADM variables 3.4.2 What does this mean? Dynamics 3.4.3 Ashtekar connection and triads 3.5 Euclidean general relativity in three spacetime dimensions 3.6 Complements 3.6.1 Working with general covariant field theory 3.6.2 Problems

4 Classical discretization

4.1 Lattice QCD 4.1.1 Hamiltonian lattice theory 4.2 Discretization of covariant systems 4.3 Regge calculus 4.4 Discretization of general relativity on a two-complex 4.5 Complements 4.5.1 Holonomy 4.5.2 Problems

Part II THREE-DIMENSIONAL THEORY

5 Three-dimensional euclidean theory

5.1 Quantization strategy 5.2 Quantum kinematics: Hilbert space 5.2.1 Length quantization 5.2.2 Spin networks 5.3 Quantum dynamics: transition amplitudes 5.3.1 Properties of the amplitude 5.3.2 Ponzano–Regge model 5.4 Complements 5.4.1 Elementary harmonic analysis 5.4.2 Alternative form of the transition amplitude 5.4.3 Poisson brackets 5.4.4 Perimeter of the universe

6 Bubbles and the cosmological constant

6.1 Vertex amplitude as gauge-invariant identity 6.2 Bubbles and spikes 6.3 Turaev–Viro amplitude 6.3.1 Cosmological constant 6.4 Complements 6.4.1 A few notes on SU(2)q 6.4.2 Problem

Part III THE REAL WORLD

7 The real world: four-dimensional lorentzian theory

7.1 Classical discretization 7.2 Quantum states of gravity 7.2.1 Yγ map 7.2.2 Spin networks in the physical theory 7.2.3 Quanta of space 7.3 Transition amplitudes 7.3.1 Continuum limit 7.3.2 Relation with QED and QCD 7.4 Full theory 7.4.1 Face amplitude, wedge amplitude, and the kernel P 7.4.2 Cosmological constant and IR finiteness 7.4.3 Variants 7.5 Complements 7.5.1 Summary of the theory 7.5.2 Computing with spin networks 7.5.3 Spectrum of the volume 7.5.4 Unitary representation of the Lorentz group and the Yγ map

8 Classical limit

8.1 Intrinsic coherent states 8.1.1 Tetrahedron geometry and SU(2) coherent states 8.1.2 Livine–Speziale coherent intertwiners 8.1.3 Thin and thick wedges and time-oriented tetrahedra 8.2 Spinors and their magic 8.2.1 Spinors, vectors, and bivectors 8.2.2 Coherent states and spinors 8.2.3 Representations of SU(2) and SL(2,C) on functions of spinors and Yγ map 8.3 Classical limit of the vertex amplitude 8.3.1 Transition amplitude in terms of coherent states 8.3.2 Classical limit versus continuum limit 8.4 Extrinsic coherent states

9 Matter

9.1 Fermions 9.2 Yang–Mills fields

Part IV PHYSICAL APPLICATIONS

10 Black holes

10.1 Bekenstein–Hawking entropy 10.2 Local thermodynamics and Frodden–Ghosh–Perez energy 10.3 Kinematical derivation of the entropy 10.4 Dynamical derivation of the entropy 10.4.1 Entanglement entropy and area fluctuations 10.5 Complements 10.5.1 Accelerated observers in Minkowski and Schwarzschild metrics 10.5.2 Tolman law and thermal time 10.5.3 Algebraic quantum theory 10.5.4 KMS and thermometers 10.5.5 General covariant statistical mechanics and quantum gravity

11 Cosmology

11.1 Classical cosmology 11.2 Canonical loop quantum cosmology 11.3 Spinfoam cosmology 11.3.1 Homogeneous and isotropic geometry 11.3.2 Vertex expansion 11.3.3 Large-spin expansion 11.4 Maximal acceleration 11.5 Physical predictions?

12 Scattering

12.1 n-Point functions in general covariant theories 12.2 Graviton propagator

13 Final remarks

13.1 Brief historical note 13.2 What is missing

References Index