Testing the master constraint programme for loop quantum gravity: II. Finite-dimensional systems

2004/11/29 by Bianca Dittrich, Thomas Thiemann · 9 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Constraint (computer-aided design) #Cosmology and Gravitation Theories #Geometry #Hamiltonian (control theory) #Hamiltonian constraint #Loop (graph theory) #Loop quantum cosmology #Loop quantum gravity #Mathematical optimization #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum gravity #Quantum mechanics #Series (stratigraphy) #Theoretical physics #Wheeler–DeWitt equation #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0264-9381/23/4/002

published as Class.Quant.Grav. 23 (2006) 1067-1088 · 23 pages, no figures

arxiv created 2004/11/29 · openalex publication_date 2006/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This is the second paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we begin with the simplest examples: Finite dimensional models with a finite number of first or second class constraints, Abelean or non -- Abelean, with or without structure functions.

Citations

• Testing the master constraint programme for loop quantum gravity: I. General framework
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Testing the master constraint programme for loop quantum gravity: IV. Free field theories
• Partial and complete observables for Hamiltonian constrained systems
• Loop Quantum Gravity
• On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories
• The Phoenix Project: master constraint programme for loop quantum gravity
• Lectures on Loop Quantum Gravity

Cited by

• Algebraic quantum gravity (AQG): II. Semiclassical analysis
• Testing the master constraint programme for loop quantum gravity: V. Interacting field theories
• The Phoenix Project: master constraint programme for loop quantum gravity
• A path integral for the master constraint of loop quantum gravity
• Approximating the physical inner product of loop quantum cosmology
• Testing the master constraint programme for loop quantum gravity: III. models
• Emergent diffeomorphism invariance in a discrete loop quantum gravity model
• Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory
• Loop Quantum Gravity: An Inside View
• Loop quantum gravity [wikipedia]