Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables

Abstract

This bibliography attempts to give a comprehensive overview of all the literature related to the Ashtekar connection and the Rovelli-Smolin loop variables. The original version was compiled by Peter Hübner in 1989, and it has been subsequently updated by Gabriela Gonzalez, Bernd Brügmann, Monica Pierri, Troy Schilling, Alejandro Corichi and Christopher Beetle. Information about additional literature, new preprints, and especially corrections are always welcome.

arXiv comment25 pages, latex file

References in corpus (92)

• The Cosmological Constant
• Discreteness of area and volume in quantum gravity
• Quantum Theory of Gravity I: Area Operators
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Black Hole Entropy from Loop Quantum Gravity
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Weaving a classical geometry with quantum threads
• Projective Techniques and Functional Integration
• Spin Network States in Gauge Theory
• The physical hamiltonian in nonperturbative quantum gravity
• Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Counting surface states in the loop quantum gravity
• Generalized Measures in Gauge Theory
• Representation Theory of Analytic Holonomy C* Algebras
• Link Invariants of Finite Type and Perturbation Theory
• Consequences of Propagating Torsion in Connection-Dynamic Theories of Gravity
• Jones Polynomials for Intersecting Knots as Physical States of Quantum Gravity
• Reality Conditions and Ashtekar Variables: a Different Perspective
• Gravitons and Loops
• A left-handed simplicial action for euclidean general relativity
• From Euclidean to Lorentzian General Relativity: The Real Way
• The geometry of quantum spin networks
• A Real Polynomial Formulation of General Relativity in terms of Connections
• Physics with nonperturbative quantum gravity: radiation from a quantum black hole
• Unification of Gravity and Yang-Mills Theory in (2+1)-Dimensions
• Recent Developments in Non-Perturbative Quantum Gravity
• On the relation between the connection and the loop representation of quantum gravity
• Self-dual gravity as a two dimensional theory and conservation laws
• The Non-perturbative Canonical Quantization of the N=1 Supergravity
• Solution space of 2+1 gravity on $\mathbf{R}\times T^2$ in Witten's connection formulation
• Self-dual gravity and the chiral model
• Unique determination of an inner product by adjointness relations in the algebra of quantum observables
• The future of spin networks
• Integration on the space of Connections Modulo Gauge Transformations
• Spacetime Covariant Form of Ashtekar's Constraints
• Topological Field Theory As The Key To Quantum Gravity
• Superspace Dynamics and Perturbations Around "Emptiness"
• Reality conditions for Ashtekar variables as Dirac constraints
• Extended Loops: A New Arena for Nonperturbative Quantum Gravity
• Covariant Phase Space Formulation of Parametrized Field Theories
• Spin Networks and Recoupling in Loop Quantum Gravity
• The weaving of curved geometries
• Lattice knot theory and quantum gravity in the loop representation
• A real alternative to quantum gravity in loop space
• Self Duality and Quantization
• Variational derivation of exact skein relations from Chern--Simons theories
• Observables for spacetimes with two Killing field symmetries
• The Standard Model with gravity couplings
• Is the third coefficient of the Jones knot polynomial a quantum state of gravity?
• Quantum Loop Representation for Fermions coupled to Einstein-Maxwell field
• Gauss Linking Number and Electro-magnetic Uncertainty Principle
• Loop Variable Inequalities in Gravity and Gauge Theory
• Regularization of the Hamiltonian constraint and the closure of the constraint algebra
• The Spin Holonomy Group In General Relativity
• The space of states of quantum gravity in terms of loops and extended loops: some remarks
• Experimental Signatures of Quantum Gravity
• Recent Mathematical Developments in Quantum General Relativity
• Minisuperspaces: Symmetries and Quantization
• Geometric Structures and Loop Variables in (2+1)-Dimensional Gravity
• Ashtekar's New Variables and Positive Energy
• Functional Integration on Spaces of Connections
• Minisuperspace Examples of Quantization Using Canonical Variables of the Ashtekar Type: Structure and Solutions
• Non-Minimally Coupled Scalar Field and Ashtekar Variables
• The Path Integral for the Loop Representation of Lattice Gauge Theories
• The Geroch group in the Ashtekar formulation
• The Affine symmetry of self-dual gravity
• The general solution of the quantum Einstein equations?
• Recent Developments in Classical and Quantum Theories of Connections, Including General Relativity
• Open-Flux Solutions to the Constraints for Plane Gravity Waves
• Extended knots and the space of states of quantum gravity
• On the solution of the initial value constraints for general relativity coupled to matter in terms of Ashtekar's variables
• The Gauss Linking Number in Quantum Gravity
• Closed-Flux Solutions to the Constraints for Plane Gravity Waves
• Knot Invariants for Intersecting Loops
• BRST cohomology of Yang-Mills gauge fields in the presence of gravity in Ashtekar variables
• Chern-Simons functional and the no-boundary proposal in Bianchi IX quantum cosmology
• Differential Geometry for the Space of Connections Modulo Gauge Transformations
• Ashtekar's Approach to Quantum Gravity
• Cosmological "Ground State" Wave Functions in Gravity and Electromagnetism
• Mixmaster quantum cosmology in terms of physical dynamics
• Representations of the $SU(N)$ $T$-algebra and the loop representation in $1+1$-dimensions
• Classical analysis of Bianchi types I and II in Ashtekar variables
• Mtric from Non-Metric Action of Gravity
• General covariance, and supersymmetry without supersymmetry
• Reduced phase space quantization of Ashtekar's gravity on de Sitter background
• Mathematical Problems of Quantum Gravity
• Induced Topology on the Hoop Group
• Ashtekar Constraint Surface as Projection of Hilbert-Palatini One
• A Hopf Algebra Structure in Self-dual Gravity
• The Gauss Constraint in the Extended Loop Representation
• Quantum Field Theory of Geometry

Cited by in corpus (4)

• Loop quantum gravity and light propagation
• Quantum gravity and spin 1/2 particles effective dynamics
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Consistency of Orthodox Gravity