Twistor quantisation and curved space-time | SpringerLinkTwistorial applications abound and are presented in great detail. The approach here is to show how problems with the standard physical framework may be solved using new twistorial techniques. Preface; Summary of volume 1; 6. Twistors; 7. Null congruences; 8. Classification of curvature tensors; 9.
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Twistor theory was proposed by Roger Penrose in  as a possible path  to quantum gravity and has evolved into a branch of theoretical and mathematical physics. Penrose proposed that twistor space should be the basic arena for physics from which space-time itself should emerge. It leads to a powerful set of mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory and in physics to relativity and quantum field theory, in particular to scattering amplitudes. Physically it has the interpretation as the space of massless particles with spin. This definition can be extended to arbitrary dimensions except that beyond dimension four, one defines projective twistor space to be the space of projective pure spinors for the conformal group. In its original form, twistor theory encodes physical fields on Minkowski space into complex analytic objects on twistor space via the Penrose transform. This is especially natural for massless fields of arbitrary spin.