The Further Advances in Twistor Theory: v. 1(Pitman Research Notes in Mathematics Series)

Twistor theory is the mathematical framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory. It has since developed into a broad many-faceted programme that attempts to resolve basic problems in physics by encoding the structure of physical fields and indeed space-time itself into the complex analytic geometry of twistor space. Twistor theory has applications in areas of mathematics and mathematical physics. These include powerful techniques for the solution of self-duality equations both for the Yang-Mills and the Einstein equations, new approaches to the representation theory of Lie groups and the quasi-local definition of mass in general relativity, to name but a few. This volume, "The Penrose transform and its applications" and its companion volume, "Twistors in curved space-time", comprise an abundance of new material, including a collection of "Twistor Newsletter" articles written over a period of ten years. These trace the development of the twistor programme and its applications over that period and offer an overview on the current status of various aspects of the programme. The articles have been written in an informal and easy-to-read style and have been arranged by the editors into chapters which have been supplemented with detailed introductions, making the volumes self-contained and accessible to graduate students and non-specialists from other fields.

Table of Contents:
Part 1 An overview of twistor theory: general background, L.J.Mason; mathematical background, L.J.Mason. Part 2 Concrete approaches to the Penrose transform: contour integral formulae old and new, L.J.Mason and L.P.Hughston; ambi-twistors, M.G.Eastwood; the wave equation in even dimensions, L.P.Hughston; extensions of massless fields into CP5, L.P.Hughston and T.R.Hurd; conformal weight and spin bundles, L.P.Hughston and T.R.Hurd; "mini-twistors", P.E.Jones; a remarkable connnection between the wave equation and spinors in higher dimensions, L.P.Hughston; the Penrose transform without cohomology, M.G.Eastwood; on closed-set coverings for PT+, R.Penrose; applications of the geometry of SO(8) spinors to Laplace's equation in 6 dimensions, L.P.Hughston; cohomology of the quadric and homogenous zero rest mass fields, P.E.Jones; a note on background coupled massless fields, A.Helfer; Maxwell fields on a self-dual gravitational background, C.Kozameh et al; Dolbeault representatives from characteristic data at null infinity, L.J.Mason; local twistors and the Penrose transform for homogenous bundles, L.J.Mason; the relationship between spin-2 fields, linearized gravity and linearized conformal gravity, L.J.Mason; on Ward's integral formula for plane wave space-times, L.J.Mason. Part 3 Abstract approaches to the Penrose transform: the tip of the iceberg, M.G.Eastwood; what is the Penrose transform?, M.A.Singer; on non-projective twistor cohomology, M.G.Eastwood; a generalized deRham sequence, N.P.Buchdahl; the inverse twistor function revisited, N.P.Buchdahl; anti-twistor functions, R.Josza; twistors versus anti-twistors, M.G.Eastwood; a note on the wave equation, N.P.Buchdahl; spinors and complex geometry in higher dimensions, S.B.Petrack; on the density of elementary states, M.G.Eastwood and A.Pilato; the Penrose transform for homogeneous bundles, M.G.Eastwood; the twistor transform and conformally invariant operators, M.A.Singer; on Michael Murray's twistor correspondence, M.G.Eastwood; on the topology of families of manifolds and the pullback mechanism, M.A.Singer; the Penrose transform for complex homogeneous spaces, M.G.Eastwood; the twistor realization of the discrete series, M.G.Eastwood; local cohomolgy, elementary states and evaluation, R.J.Baston; a twistor transform for the discrete series - the case of SU(1,2), E.Dunne and M.G.Eastwood. Part 4 Twistor theory and elementary particle physics. (Part Contents)