Elementary states, supergeometry and twistor theory
<p>It is shown that H<sup>p-1</sup> (P<sup>+</sup>, <em>0</em> (-m-p)) is a Fréchet space, and its dual is H<sup>q-1</sup>(P<sup>-</sup>, <em>0</em> (m-q)), where P<sup>+</sup> and P<sup>-</sup> ar...
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| Формат: | Дисертація |
| Мова: | English |
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1986
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| _version_ | 1826299406923595776 |
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| author | Pilato, A Pilato, Alejandro |
| author2 | Penrose, R |
| author_facet | Penrose, R Pilato, A Pilato, Alejandro |
| author_sort | Pilato, A |
| collection | OXFORD |
| description | <p>It is shown that H<sup>p-1</sup> (P<sup>+</sup>, <em>0</em> (-m-p)) is a Fréchet space, and its dual is H<sup>q-1</sup>(P<sup>-</sup>, <em>0</em> (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 <em>0</em>(-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>, <em>0</em>(-m-p)).</p> <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.</p> |
| first_indexed | 2024-03-07T05:01:28Z |
| format | Thesis |
| id | oxford-uuid:d86c78d7-2e6e-4a5c-a37a-81d8dbf3ccd8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:01:28Z |
| publishDate | 1986 |
| record_format | dspace |
| spelling | oxford-uuid:d86c78d7-2e6e-4a5c-a37a-81d8dbf3ccd82022-03-27T08:48:26ZElementary states, supergeometry and twistor theoryThesishttp://purl.org/coar/resource_type/c_db06uuid:d86c78d7-2e6e-4a5c-a37a-81d8dbf3ccd8Twistor theorySupermanifolds (Mathematics)EnglishPolonsky Theses Digitisation Project1986Pilato, APilato, AlejandroPenrose, REastwood, MPenrose, REastwood, M<p>It is shown that H<sup>p-1</sup> (P<sup>+</sup>, <em>0</em> (-m-p)) is a Fréchet space, and its dual is H<sup>q-1</sup>(P<sup>-</sup>, <em>0</em> (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 <em>0</em>(-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>, <em>0</em>(-m-p)).</p> <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.</p> |
| spellingShingle | Twistor theory Supermanifolds (Mathematics) Pilato, A Pilato, Alejandro Elementary states, supergeometry and twistor theory |
| title | Elementary states, supergeometry and twistor theory |
| title_full | Elementary states, supergeometry and twistor theory |
| title_fullStr | Elementary states, supergeometry and twistor theory |
| title_full_unstemmed | Elementary states, supergeometry and twistor theory |
| title_short | Elementary states, supergeometry and twistor theory |
| title_sort | elementary states supergeometry and twistor theory |
| topic | Twistor theory Supermanifolds (Mathematics) |
| work_keys_str_mv | AT pilatoa elementarystatessupergeometryandtwistortheory AT pilatoalejandro elementarystatessupergeometryandtwistortheory |