Emergent diffeomorphism invariance in a discrete loop quantum gravity model
Abstract
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 firstclass algebra of constraints of the continuum theory becomes second class upon discretization. If one treats the secondclass 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 onedimensional model and complete the quantization using uniform discretizations. The model can be viewed as a spherically symmetric reduction of the wellknown 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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 February 2009
 DOI:
 10.1088/02649381/26/3/035002
 arXiv:
 arXiv:0807.2808
 Bibcode:
 2009CQGra..26c5002G
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 12 pages, Revtex