2008/07/17 by Rodolfo Gambini, Jorge Pullin · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Topics in Algebra #Diffeomorphism #Discretization #General covariance #Invariant (physics) #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #Quantum #Quantum gravity #gr-qc
paper · pdf · doi:10.1088/0264-9381/26/3/035002
published as Class.Quant.Grav.26:035002,2009 · 12 pages, Revtex
arxiv created 2008/07/17 · openalex publication_date 2009/01/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first-class algebra of constraints of the continuum theory becomes second class upon discretization. If one treats the second-class constraints properly, the resulting theories have very different dynamics and number of degrees of freedom than those of the continuum theory. It is therefore questionable how these theories could be considered a starting point for the quantization and the definition of a continuum theory through a continuum limit. We show explicitly in a model that the uniform discretizations approach to the quantization of constrained systems overcomes these difficulties. We consider here a simple diffeomorphism invariant one-dimensional model and complete the quantization using uniform discretizations. The model can be viewed as a spherically symmetric reduction of the well-known Husain–Kuchař model of diffeomorphism invariant theory. We show that the correct quantum continuum limit can be satisfactorily constructed for this model. This opens the possibility of treating (1 + 1)-dimensional dynamical situations of great interest in quantum gravity taking into account the full dynamics of the theory and preserving the spacetime covariance at a quantum level.