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Title: Curved twistor spaces
Author: Ward, R. S.
ISNI:       0000 0001 3563 2444
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1977
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This thesis is concerned with the problem of "coding" the information of various zero-rest-mass fields into the complex structure of "curved twistor spaces". Chapter 2 is devoted to various preliminaries: a brief outline of twistor theory; an introduction to vector bundles and sheaf cohomology and some of their applications in twistor theory; and a discussion of potentials for electromagnetic fields. Chapter 3 deals with left-handed (i.e. anti-self-dual) electromagnetic fields and describes in some detail the associated curved twistor spaces. It is shown how holomorphic functions on the curved spaces give rise to "charged" zero-rest-mass fields on space-time. The first section of Chapter 4 gives the corresponding results for left-handed gravitational fields, using Penrose's "nonlinear graviton" construction. The rest of Chapter 4 is devoted to the concept of twistors relative to a hypersurface in a general curved space-time. In §4.2 the hypersurface is taken to be spacelike; the hypersurface twistors are described and the problem of using holomorphic hypersurface twistor functions to generate fields on the hypersurface and in space-time is discussed. Next the hypersurface is taken to be null. The structure of the associated hypersurface twistor space and and H-space are described in some detail. The twistor space has a natural inner product and, if the hypersurface is shear-free, then it has a "fibred" structure as well. In §4.4 the hypersurface twistor language is used to show that the propagation of twistors through an analytic pp-wave is given by the unfolding of a canonical transformation. Chapter 5 extends the "electromagnetic" construction of Chapter 3 to non-Abelian gauge theories; left-handed gauge fields are described in terms of complex vector bundles over protective twistor space.
Supervisor: Penrose, R. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available