Twisted geometries, twistors, and conformal transformations

Show simple item record Långvik, Miklos Speziale, Simone 2017-05-12T10:16:01Z 2017-05-12T10:16:01Z 2016-07-26
dc.identifier.citation Långvik , M & Speziale , S 2016 , ' Twisted geometries, twistors, and conformal transformations ' , Physical Review D , vol. 94 , no. 2 , 024050 .
dc.identifier.other PURE: 69262234
dc.identifier.other PURE UUID: 33d6425c-cd1f-40ba-8b52-ff0658191d2a
dc.identifier.other WOS: 000381492700006
dc.identifier.other Scopus: 84979649150
dc.description.abstract The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a timelike direction singled out. The isomorphism depends on the Immirzi parameter gamma and reduces to the identity for gamma = infinity. Using this twistorial representation, we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a one-parameter family of embeddings of T*SL(2, C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one-that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view and compare it with a discretization of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuum limit, the latter reproduces the same transformation of the extrinsic geometry, while also rescaling the areas and volumes and preserving the angles associated with the intrinsic geometry. Away from the continuum limit, its action has an interesting nonlinear structure but is in general incompatible with the closure constraint needed for the geometric interpretation. As a side result, we compute the precise relation between the extrinsic geometry used in twisted geometries and the one defined in the gauge-invariant parametrization by Dittrich and Ryan and show that the secondary simplicity constraints they posited coincide with those dynamically derived in the toy model of [Classical Quantum Gravity 32, 195015 (2015)]. en
dc.format.extent 18
dc.language.iso eng
dc.relation.ispartof Physical Review D
dc.rights cc_by
dc.rights.uri info:eu-repo/semantics/openAccess
dc.subject SPIN NETWORKS
dc.subject SPACE
dc.subject MODEL
dc.subject 114 Physical sciences
dc.title Twisted geometries, twistors, and conformal transformations en
dc.type Article
dc.contributor.organization Department of Physics
dc.description.reviewstatus Peer reviewed
dc.relation.issn 2470-0010
dc.rights.accesslevel openAccess
dc.type.version publishedVersion

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