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13040104

I will describe recent work in collaboration with Adam

Henderson, Alok Laddha, and Madhavan Varadarajan on the loop quantization of a

certain $G_{\mathrm{N}}\rightarrow 0$ limit of Euclidean gravity, introduced by

Smolin. The model allows one to test various quantization choices one is faced

with in loop quantum gravity, but in a simplified setting. The main results are the construction of

finite-triangulation Hamiltonian and diffeomorphism constraint operators whose

continuum limits can be evaluated in a precise sense, such that the quantum

Dirac algebra of constraints closes nontrivially and free of anomalies. The construction relies heavily on techniques

of Thiemann's QSD treatment, and lessons learned applying such techniques to

the loop quantization of parameterized scalar field theory and the

diffeomorphism constraint in loop quantum gravity. I will also briefly discuss the status of the

quantum constraint algebra in full LQG, and how some of the lessons learned from

the present model may guide us in that setting.

©2012 Perimeter Institute for Theoretical Physics