Title:	Constraint algebra in Smolins' G→0 limit of 4D Euclidean gravity
Authors:	Varadarajan, Madhavan
Issue Date:	14-May-2018
Publisher:	American Physical Society
Citation:	Physical Review D, 2018, Vol. 97, p106007
Abstract:	Smolin’s generally covariant G Newton → 0 limit of 4d Euclidean gravity is a useful toy model for the study of the constraint algebra in loop quantum gravity (LQG). In particular, the commutator between its Hamiltonian constraints has a metric dependent structure function. While a prior LQG-like construction of nontrivial anomaly free constraint commutators for the model exists, that work suffers from two defects. First, Smolin’s remarks on the inability of the quantum dynamics to generate propagation effects apply. Second, the construction only yields the action of a single Hamiltonian constraint together with the action of its commutator through a continuum limit of corresponding discrete approximants; the continuum limit of a product of two or more constraints does not exist. Here, we incorporate changes in the quantum dynamics through structural modifications in the choice of discrete approximants to the quantum Hamiltonian constraint. The new structure is motivated by that responsible for propagation in an LQG-like quantization of paramatrized field theory and significantly alters the space of physical states. We study the off shell constraint algebra of the model in the context of these structural changes and show that the continuum limit action of multiple products of Hamiltonian constraints is (a) supported on an appropriate domain of states, (b) yields anomaly free commutators between pairs of Hamiltonian constraints, and (c) is diffeomorphism covariant. Many of our considerations seem robust enough to be applied to the setting of 4d Euclidean gravity.
Description:	Open Access
URI:	http://hdl.handle.net/2289/6928
ISSN:	1550-7998 1550-2368(Online)
Alternative Location:	http://adsabs.harvard.edu/abs/2018PhRvD..97j6007V https://arxiv.org/abs/1802.07033 https://doi.org/10.1103/PhysRevD.97.106007
Copyright:	2018 American Physical Society
Appears in Collections:	Research Papers (TP)

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