Website Search
Find information on spaces, staff, and services.
Catalog Search
Books
Loop Quantum Gravity for the Bewildered : The Self-Dual Approach Revisited
- Author / Creator
- Available as
- Online
Details
- Creator
- Sundance Bilson-Thompson and Deepak Vaid
- Format
- Books
- Language
- English
- Contributors
- Publication
-
- Second edition
- Cham, Switzerland : Springer, Springer Nature Switzerland AG, [2024]
- ©2017
- Physical Details
-
- 1 online resource (210 pages)
- ISBNs
- 9783031434525, 3031434528, 303143451X
- Intro -- Preface -- Conventions -- Indices -- Symbols -- Contents -- Acronyms -- 1 Introduction -- 1.1 Motivation and Some History -- 1.2 Overview: Loop Quantum Gravity and Friends -- 2 Classical GR -- 2.1 Parallel Transport and Curvature -- 2.2 Einstein's Field Equations -- 2.3 Coordinates and Diffeomorphism Invariance -- 3 Quantum Field Theory -- 3.1 Covariant Derivative and Curvature -- 3.2 Dual Tensors, Bivectors and k-forms -- 3.3 Wilson Loops and Holonomies -- 3.4 Dynamics of Quantum Fields -- 4 Expanding on Classical GR -- 4.1 Lagrangian Approach: The Einstein-Hilbert Action -- 4.2 Hamiltonian Approach: The ADM Splitting -- 4.2.1 Physical Interpretation of Constraints -- 4.3 Seeking a Path to Canonical Quantum Gravity -- 4.3.1 Connection Formulation -- 4.3.2 Tetrads -- 4.3.3 Choosing a Gauge Group -- 4.3.4 Spin Connection -- 4.3.5 Palatini Action -- 4.3.6 Palatini Hamiltonian and Constraints -- 5 First Steps to a Theory of Quantum Gravity -- 5.1 Ashtekar Formulation: ``New Variables'' for General Relativity -- 5.2 The Barbero-Immirzi Parameter -- 5.3 To Be or Not to Be (Real) -- 5.4 Loop Quantization -- 5.5 Canonical Quantization -- 6 Kinematical Hilbert Space -- 6.1 Kinematics via a Toy Model -- 6.2 Space of Generalised Connections -- 6.3 Area Operator -- 6.4 Volume Operator -- 6.5 Spin Networks -- 6.6 Looking Ahead to Spin Foams -- 7 Dynamics of Spin Networks -- 7.1 Spin Foams -- 7.1.1 Transition Amplitudes -- 7.2 Early Developments -- 7.2.1 BF Theory -- 7.2.2 Chern-Simons Theory -- 7.2.3 The Cosmological Constant -- 7.3 Some Recent Developments -- 7.3.1 Tensor Networks -- 7.3.2 Spinorial LQG and Coherent States -- 7.3.3 Group Field Theory -- 8 Applications -- 8.1 Black Hole Entropy -- 8.1.1 Rovelli's Counting -- 8.1.2 Number Theoretical Approach -- 8.1.3 Chern-Simons Approach -- 8.1.4 Entropy from Entanglement
- 8.2 Loop Quantum Cosmology -- 8.2.1 Isotropy and Homogeneity in the Metric Formulation -- 8.2.2 FLRW Models -- 8.2.3 Connection Variables -- 8.2.4 Holonomy Variables -- 8.2.5 Quantisation -- 8.2.6 Triad Eigenstates and Volume Quantization -- 8.2.7 Regularized FLRW Hamiltonian -- 8.2.8 Singularity Resolution and Bouncing Cosmologies -- 9 Discussion -- A Groups, Representations, and Algebras -- A.1 Lie Groups and Algebras -- A.2 Lorentz Lie-Algebra -- B Blades, Forms, and Duality -- B.1 Blades and Multivectors -- B.2 Differential Forms and the Exterior Derivative -- B.3 Duality -- B.4 Field Strength and the Exterior Derivative -- B.5 Spacetime Duality -- B.6 Lie-Algebra Duality -- B.7 Yang-Mills -- B.8 Geometrical Interpretation -- B.9 (Anti) Self-dual Connections -- C Path Ordered Exponential -- D ADM Variables -- D.1 Covariant Spatial Derivative -- D.2 Extrinsic Curvature -- D.3 Canonical Momentum in the ADM Formulation -- E Lie Derivative -- F 3+1 Decomposition of the Palatini Action -- G The Kodama State -- H Peter-Weyl Theorem -- I Regge Calculus -- J Fibre Bundles -- K Knots, Links, and the Kauffman Bracket -- L Quantum (or q-Deformed) Groups -- M Entropy -- N Square-Free Numbers -- O Brahmagupta-Pell Equation -- O.1 Quadratic Integers and the BP Equation