Quantisation of twistor theory by cocycle twist

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dc.creatorBrain, S.
dc.creatorMajid, S.
dc.date2007-01-30
dc.date2007-03-20
dc.date.accessioned2026-07-07T11:59:50Z
dc.date.available2026-07-07T11:59:50Z
dc.descriptionWe present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra form which we can then `quantise' by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor space CP^3, compactified Minkowski space CMh and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we show that the pull-back of the tautological bundle on CMh pulls back to the basic instanton on S^4\subset CMh and that this observation quantises to obtain the Connes-Landi instanton on θ-deformed S^4 as the pull-back of the tautological bundle on our θ-deformed CMh. We likewise quantise the fibration CP^3--> S^4 and use it to construct the bundle on θ-deformed CP^3 that maps over under the transform to the θ-deformed instanton.
dc.description68 pages 0 figures. Significant revision now has detailed formulae for classical and quantum CP^3
dc.identifierhttps://arxiv.org/abs/math/0701893
dc.identifierhttp://arxiv.org/abs/math/0701893
dc.identifierCommun.Math.Phys.284:713-774,2008
dc.identifierdoi:10.1007/s00220-008-0607-1
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/206708
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.titleQuantisation of twistor theory by cocycle twist
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