title: Palatial twistor theory and the twistor googly problem.
abstract: A key obstruction to the twistor programme has been its so-called 'googly problem', unresolved for nearly 40 years, which asks for a twistor description of right-handed interacting massless fields (positive helicity), using the same twistor conventions that give rise to left-handed fields (negative helicity) in the standard 'nonlinear graviton' and Ward constructions. An explicit proposal for resolving this obstruction--palatial twistor theory--is put forward (illustrated in the case of gravitation). This incorporates the concept of a non-commutative holomorphic quantized twistor 'Heisenberg algebra', extending the sheaves of holomorphic functions of conventional twistor theory to include the operators of twistor differentiation.
authors.affiliation: Mathematical Institute, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK penroad@nexus.ox.ac.uk.
authors.forename: Roger
authors.initials: R
authors.lastname: Penrose
keywords: Einstein equations; curved space–times; non-commutative geometry; twistor theory