Title:	From Euclidean to Lorentzian Loop Quantum Gravity via a Positive Complexifier
Authors:	Varadarajan, Madhavan
Keywords:	loop quantum gravity Wick rotation Lorentzian
Issue Date:	12-Dec-2018
Publisher:	IOP Publishing Ltd.
Citation:	Classical and Qunatum Gravity, 2019, Vol. 36,p015016
Abstract:	We construct a positive complexifier, differentiable almost everywhere on the classical phase space of real triads and SU(2) connections, which generates a Wick Transform from Euclidean to Lorentzian gravity everywhere except on a phase space set of measure zero. This Wick transform assigns an equal role to the self dual and anti-self dual Ashtekar variables in quantum theory. We argue that the appropriate quantum arena for an analysis of the properties of the Wick rotation is the diffeomorphism invariant Hilbert space of Loop Quantum Gravity (LQG) rather than its kinematic Hilbert space. We examine issues related to the construction, in quantum theory, of the positive complexifier as a positive operator on this diffeomorphism invariant Hilbert space. Assuming the existence of such an operator, we explore the possibility of identifying physical states in Lorentzian LQG as Wick rotated images of physical states in the Euclidean theory. Our considerations derive from Thiemann's remarkable proposal to define Lorentzian LQG from Euclidean LQG via the implementation in quantum theory of a phase space `Wick rotation' which maps real Ashtekar-Barbero variables to Ashtekar's complex, self dual variables.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/7117
ISSN:	1361-6382
Alternative Location:	https://arxiv.org/abs/1808.00673 https://doi.org/10.1088/1361-6382/aaf2cd
Copyright:	2019 IOP Publishing Ltd.
Appears in Collections:	Research Papers (TP)

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