Show simple item record

dc.contributor.authorGundry, James Michael
dc.date.accessioned2017-10-20T09:51:05Z
dc.date.available2017-10-20T09:51:05Z
dc.date.issued2017-10-01
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/267894
dc.description.abstractIn twistor theory the nonlinear graviton construction realises four-dimensional antiself- dual Einstein manifolds as Kodaira moduli spaces of rational curves in threedimensional complex manifolds. We establish a Newtonian analogue of this procedure, in which four-dimensional Newton-Cartan manifolds arise as Kodaira moduli spaces of rational curves with normal bundle O + O(2) in three-dimensional complex manifolds. The isomorphism class of the normal bundle is unstable with respect to general deformations of the complex structure, exhibiting a jump to the Gibbons- Hawking class of twistor spaces. We show how Newton-Cartan connections can be constructed on the moduli space by means of a splitting procedure augmented by an additional vector bundle on the twistor space which emerges when considering the Newtonian limit of Gibbons-Hawking manifolds. The Newtonian limit is thus established as a jumping phenomenon. Newtonian twistor theory is extended to dimensions three and five, where novel features emerge. In both cases we are able to construct Kodaira deformations of the flat models whose moduli spaces possess Galilean structures with torsion. In five dimensions we find that the canonical affine connection induced on the moduli space can possess anti-self-dual generalised Coriolis forces. We give examples of anti-self-dual Ricci-flat manifolds whose twistor spaces contain rational curves whose normal bundles suffer jumps to O(2 - k) + O(k) for arbitrarily large integers k, and we construct maps which portray these big-jumping twistor spaces as the resolutions of singular twistor spaces in canonical Gibbons-Hawking form. For k > 3 the moduli space itself is singular, arising as a variety in an ambient complex space. We explicitly construct Newtonian twistor spaces suffering similar jumps. Finally we prove several theorems relating the first-order and higher-order symmetry operators of the Schrödinger equation to tensors on Newton-Cartan backgrounds, defining a Schrödinger-Killing tensor for this purpose. We also explore the role of conformal symmetries in Newtonian twistor theory in three, four, and five dimensions.
dc.description.sponsorshipSTFC
dc.language.isoen
dc.rightsNo Creative Commons licence (All rights reserved)
dc.subjectTwistor Theory
dc.subjectGeometry
dc.subjectMathematical Physics
dc.titleNewtonian Twistor Theory
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentDAMTP
dc.date.updated2017-10-19T20:10:31Z
dc.identifier.doi10.17863/CAM.13822
dc.publisher.collegeTrinity College
dc.type.qualificationtitlePhD in Applied Mathematics and Theoretical Physics
cam.supervisorDunajski, Maciej


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record