Title:	Propagation in polymer parameterised field theory
Authors:	Varadarajan, Madhavan
Keywords:	loop quantum gravity general convariance
Issue Date:	Jan-2017
Publisher:	IOP Publishing Ltd.
Citation:	Classical and Quantum Gravity, 2017, Vol.34, p015012
Abstract:	The Hamiltonian constraint operator in loop quantum gravity acts ultralocally. Smolin has argued that this ultralocality seems incompatible with the existence of a quantum dynamics which propagates perturbations between macroscopically seperated regions of quantum geometry. We present evidence to the contrary within an LQG type 'polymer' quantization of two dimensional parameterised field theory (PFT). PFT is a generally covariant reformulation of free field propagation on flat spacetime. We show explicitly that while, as in LQG, the Hamiltonian constraint operator in PFT acts ultralocally, states in the joint kernel of the Hamiltonian and diffeomorphism constraints of PFT necessarily describe propagation effects. The particular structure of the finite triangulation Hamiltonian constraint operator plays a crucial role, as does the necessity of imposing (the continuum limit of) its kinematic adjoint as a constraint. Propagation is seen as a property encoded by physical states in the kernel of the constraints rather than that of repeated actions of the finite triangulation Hamiltonian constraint on kinematic states. The analysis yields robust structural lessons for putative constructions of the Hamiltonian constraint in LQG for which ultralocal action co-exists with a description of propagation effects by physical states.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/6732
ISSN:	0264-9381 1361-6382 (E)
Alternative Location:	http://arxiv.org/abs/1609.06034 http://dx.doi.org/10.1088/1361-6382/34/1/015012 http://adsabs.harvard.edu/abs/2017CQGra..34a5012V
Copyright:	2016 IOP Publishing Ltd.
Appears in Collections:	Research Papers (TP)

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