Testing the master constraint programme for loop quantum gravity: IV. Free field theories

2004/11/29 by Bianca Dittrich, Thomas Thiemann · 10 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Constraint (computer-aided design) #Cosmology and Gravitation Theories #Hamiltonian (control theory) #Hamiltonian constraint #Loop quantum gravity #Master equation #Mathematical optimization #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Physics #Quantum #Quantum gravity #Quantum mechanics #Theoretical physics #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0264-9381/23/4/004

published as Class.Quant.Grav. 23 (2006) 1121-1142 · 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 fourth paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. We now move on to free field theories with constraints, namely Maxwell theory and linearized gravity. Since the master constraint involves squares of constraint operator valued distributions, one has to be very careful in doing that and we will see that the full flexibility of the master constraint programme must be exploited in order to arrive at sensible results.

Citations

• Testing the master constraint programme for loop quantum gravity: I. General framework
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Loop Quantum Gravity
• On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories
• 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
• On (cosmological) singularity avoidance in loop quantum gravity
• The Phoenix Project: master constraint programme for loop quantum gravity
• Testing the master constraint programme for loop quantum gravity: II. Finite-dimensional systems
• 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 [wikipedia]