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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/7117
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dc.contributor.authorVaradarajan, Madhavan-
dc.date.accessioned2019-01-15T15:12:48Z-
dc.date.available2019-01-15T15:12:48Z-
dc.date.issued2018-12-12-
dc.identifier.citationClassical and Qunatum Gravity, 2019, Vol. 36,p015016en_US
dc.identifier.issn1361-6382-
dc.identifier.urihttp://hdl.handle.net/2289/7117-
dc.descriptionRestricted Access. An open-access version is available at arXiv.org (one of the alternative locations)en_US
dc.description.abstractWe 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.en_US
dc.language.isoenen_US
dc.publisherIOP Publishing Ltd.en_US
dc.relation.urihttps://arxiv.org/abs/1808.00673en_US
dc.relation.urihttps://doi.org/10.1088/1361-6382/aaf2cden_US
dc.rights2019 IOP Publishing Ltd.en_US
dc.subjectloop quantum gravityen_US
dc.subjectWick rotationen_US
dc.subjectLorentzianen_US
dc.titleFrom Euclidean to Lorentzian Loop Quantum Gravity via a Positive Complexifieren_US
dc.typeArticleen_US
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