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Title: | Towards an anomaly-free quantum dynamics for a weak coupling limit of Euclidean gravity |
Authors: | Tomlin, Casey Varadarajan, Madhavan |
Issue Date: | 15-Feb-2013 |
Publisher: | American Physical Society |
Citation: | Physical Review D, 2013, Vol.87, p044039 |
Abstract: | The GNewton→0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)3 gauge theory. The Poisson-bracket algebra of its Hamiltonian and diffeomorphism constraints is isomorphic to that of gravity. Motivated by recent results in parametrized field theory and by the search for an anomaly-free quantum dynamics for loop quantum gravity, the quantum Hamiltonian constraint of density weight 4/3 for this U(1)3 theory is constructed so as to produce a nontrivial loop quantum gravity type representation of its Poisson brackets through the following steps. First, the constraint at finite triangulation and the commutator between a pair of such constraints are constructed as operators on the “charge” network basis. Next, the continuum limit of the commutator is evaluated with respect to an operator topology defined by a certain space of “vertex smooth” distributions. Finally, the operator corresponding to the Poisson bracket between a pair of Hamiltonian constraints is constructed at finite triangulation in such a way as to generate a “generalized” diffeomorphism and its continuum limit is shown to agree with that of the commutator between a pair of finite-triangulation Hamiltonian constraints. Our results, in conjunction with the recent work of Henderson, Laddha and Tomlin in a (2+1)-dimensional context, constitute the necessary first steps toward a satisfactory treatment of the quantum dynamics of this model. |
Description: | open Access. |
URI: | http://hdl.handle.net/2289/5553 |
ISSN: | 1550-7998 1550-2368(Online) |
Alternative Location: | http://dx.doi.org/10.1103/PhysRevD.87.044039 http://adsabs.harvard.edu/abs/2013PhRvD..87d4039T http://arxiv.org/abs/1210.6869 |
Copyright: | 2013 American Physical Society |
Appears in Collections: | Research Papers (TP) |
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