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Reference: Pilato, Alejandro Miguel., (1986). Elementary states, supergeometry and twistor theory. DPhil. University of Oxford.Citable link to this page:


Elementary states, supergeometry and twistor theory

Abstract: It is shown that Hp-1 (P+, 0 (-m-p)) is a Fréchet space, and itsdual is Hq-1(P-, 0 (m-q)), where P+ and P- are theprojectivizations of subsets of generalized twistor space(≌ ℂp-q) on which the hermitian form (of signature (p,q))is positive and negative definite respectively, and0(-m-p) denotes the sheaf of germs of holomorphic functionshomogeneous of degree -m-p. It is then proven, for p = 2and q = 2, that the subspace consisting of all twistorelementary states is dense in Hp-1(P+, 0(-m-p)).A supermanifold is a ringed space consisting of an underlyingclassical manifold and an augmented sheaf of Z2-gradedalgebras locally isomorphic to an exterior algebra. Thesubcategory of the category of ringed spaces generated bysuch supermanifolds is referred to as the super category.A mathematical framework suitable for describing thegeneralization of Yang-Mills theory to the super categoryis given. This includes explicit examples of supercoordinatechanges, superline bundles, and superconnections. Withinthis framework, a definition of the full super Yang-Millsequations is given and the simplest case is studied indetail. A comprehensive account of the generalization oftwistor theory to the super category is presented, and itis used in an attempt to formulate a complete descriptionof the super Yang-Mills equations. New concepts areintroduced, and several ideas which have previouslyappeared in the literature at the level of formal calculations are expanded and explained within a consistent framework.

Type of Award:DPhil Level of Award:Doctoral Awarding Institution: University of Oxford Notes:The digital copy of this thesis has been made available thanks to the generosity of Dr Leonard Polonsky


Penrose, RogerMore by this contributor



Eastwood, Michael G.More by this contributor



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 Bibliographic Details

Issue Date: 1986Identifiers

Urn: uuid:d86c78d7-2e6e-4a5c-a37a-81d8dbf3ccd8

Source identifier: 603835641 Item Description

Type: Thesis;

Language: eng Subjects: Twistor theory Supermanifolds (Mathematics) Tiny URL: td:603835641


Author: Pilato, Alejandro Miguel. - institutionUniversity of Oxford facultyMathematical and Physical Sciences Division facultyFaculty of

Source: https://ora.ox.ac.uk/objects/uuid:d86c78d7-2e6e-4a5c-a37a-81d8dbf3ccd8


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