Constraint algebra in Smolins' G→0 limit of 4D Euclidean gravity

Varadarajan, Madhavan

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/6928

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DC Field	Value	Language
dc.contributor.author	Varadarajan, Madhavan	-
dc.date.accessioned	2018-06-05T14:01:14Z	-
dc.date.available	2018-06-05T14:01:14Z	-
dc.date.issued	2018-05-14	-
dc.identifier.citation	Physical Review D, 2018, Vol. 97, p106007	en_US
dc.identifier.issn	1550-7998	-
dc.identifier.issn	1550-2368(Online)	-
dc.identifier.uri	http://hdl.handle.net/2289/6928	-
dc.description	Open Access	en_US
dc.description.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.	en_US
dc.language.iso	en	en_US
dc.publisher	American Physical Society	en_US
dc.relation.uri	http://adsabs.harvard.edu/abs/2018PhRvD..97j6007V	en_US
dc.relation.uri	https://arxiv.org/abs/1802.07033	en_US
dc.relation.uri	https://doi.org/10.1103/PhysRevD.97.106007	en_US
dc.rights	2018 American Physical Society	en_US
dc.title	Constraint algebra in Smolins' G→0 limit of 4D Euclidean gravity	en_US
dc.type	Article	en_US
Appears in Collections:	Research Papers (TP)

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