Twistor theory - Its aims and achievements

The essential scope of twistor theory is fully outlined and analyzed. It is noted that the basic aims of twistor theory are to provide an alternative framework for physics in which the space-time continuum and the complex continuum of quantum mechanics are merged into one and to eliminate the continuum concept from the basis of physical theory. It is also noted that in the context of the present theory, space-time points are derived objects, twistors are more basic phenomena, and quantum-mechanical uncertainties are transferred to the very concept of a space-time point. Flat-space twistors are described analytically, and the geometry of Minkowski space is reformulated in terms of the geometry of twistor space. Twistor first-quantization rules are outlined together with rules for twistor diagrams and techniques for translating analytic expressions into such diagrams. Properties of curved-space twistors are analyzed, and these twistors are identified as local, global null, hypersurface, and asymptotic twistors.