It is shown that H<sup>p-1</sup> (P<sup>+</sup>, 0 (-m-p)) is a Fréchet space, and its dual is H<sup>q-1</sup>(P<sup>-</sup>, 0 (m-q)), where P<sup>+</sup> and P<sup>-</sup> are the projectivizations of subsets of generalized twistor space (≌ ℂ<sup>p-q</sup>) on which the hermitian form (of signature (p,q)) is positive and negative definite respectively, and 0(-m-p) denotes the sheaf of germs of holomorphic functions homogeneous of degree -m-p. It is then proven, for p = 2 and q = 2, that the subspace consisting of all twistor elementary states is dense in H<sup>p-1</sup>(P<sup>+</sup>, 0(-m-p)). A supermanifold is a ringed space consisting of an underlying classical manifold and an augmented sheaf of <strong>Z</strong><sub>2</sub>-graded algebras locally isomorphic to an exterior algebra. The subcategory of the category of ringed spaces generated by such supermanifolds is referred to as the super category. A mathematical framework suitable for describing the generalization of Yang-Mills theory to the super category is given. This includes explicit examples of supercoordinate changes, superline bundles, and superconnections. Within this framework, a definition of the full super Yang-Mills equations is given and the simplest case is studied in detail. A comprehensive account of the generalization of twistor theory to the super category is presented, and it is used in an attempt to formulate a complete description of the super Yang-Mills equations. New concepts are introduced, and several ideas which have previously appeared in the literature at the level of formal calculations are expanded and explained within a consistent framework.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:235427 |
| Date | January 1986 |
| Creators | Pilato, Alejandro Miguel |
| Contributors | Penrose, Roger |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:d86c78d7-2e6e-4a5c-a37a-81d8dbf3ccd8 |
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